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Autor Vladimir I. Arnold |
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Título : Arnold's Problems Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Vladimir I. Arnold Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Número de páginas: XVI, 640 p Il.: online resource ISBN/ISSN/DL: 978-3-540-26866-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Mathematical analysis Analysis (Mathematics) Geometry History Physics Theoretical, and Computational of Sciences Clasificación: 51 Matemáticas Resumen: Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world. The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them). This book will be of great interest to researchers and graduate students in mathematics and mathematical physics En línea: http://dx.doi.org/10.1007/b138219 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35254 Arnold's Problems [documento electrónico] / SpringerLink (Online service) ; Vladimir I. Arnold . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XVI, 640 p : online resource.
ISBN : 978-3-540-26866-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Mathematical analysis Analysis (Mathematics) Geometry History Physics Theoretical, and Computational of Sciences Clasificación: 51 Matemáticas Resumen: Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world. The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them). This book will be of great interest to researchers and graduate students in mathematics and mathematical physics En línea: http://dx.doi.org/10.1007/b138219 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35254 Ejemplares
Signatura Medio Ubicación Sección Estado ningún ejemplar Catastrophe theory / Vladimir I. Arnold (1986)
Título : Catastrophe theory : with 72 figures Tipo de documento: texto impreso Autores: Vladimir I. Arnold, Autor Editorial: Berlin ; New York ; Paris : Springer Fecha de publicación: 1986 Número de páginas: IX, 108 p. Dimensiones: 20,5 cm ISBN/ISSN/DL: 978-0-387-16199-0 Idioma : Inglés (eng) Materias: Topología Clasificación: 515.1 Topología. Fractales. Catástrofes Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=5307 Catastrophe theory : with 72 figures [texto impreso] / Vladimir I. Arnold, Autor . - Berlin ; New York ; Paris : Springer, 1986 . - IX, 108 p. ; 20,5 cm.
ISBN : 978-0-387-16199-0
Idioma : Inglés (eng)
Materias: Topología Clasificación: 515.1 Topología. Fractales. Catástrofes Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=5307 Reserva
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Signatura Medio Ubicación Sección Estado 515.1 ARN cat Monografías 1ª Planta Fondo General Disponible
Título : Collected Works : Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965 Tipo de documento: documento electrónico Autores: Vladimir I. Arnold ; SpringerLink (Online service) ; Givental, Alexander B ; Khesin, Boris A ; Marsden, Jerrold E ; Varchenko, Alexander N ; Vassiliev, Victor A ; Viro, Oleg Ya ; Zakalyukin, Vladimir M Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2009 Colección: Vladimir I. Arnold - Collected Works num. 1 Número de páginas: XIII, 487 p Il.: online resource ISBN/ISSN/DL: 978-3-642-01742-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Partial differential equations Functions of real variables Physics Differential Equations Theoretical, Mathematical and Computational Real Clasificación: 51 Matemáticas Nota de contenido: On the representation of functions of two variables in the form ?[?(x) + ?(y)] -- On functions of three variables -- The mathematics workshop for schools at Moscow State University -- The school mathematics circle at Moscow State University: harmonic functions -- On the representation of functions of several variables as a superposition of functions of a smaller number of variables -- Representation of continuous functions of three variables by the superposition of continuous functions of two variables -- Some questions of approximation and representation of functions -- Kolmogorov seminar on selected questions of analysis -- On analytic maps of the circle onto itself -- Small denominators. I. Mapping of the circumference onto itself -- The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case -- Generation of almost periodic motion from a family of periodic motions -- Some remarks on flows of line elements and frames -- A test for nomographic representability using Decartes’ rectilinear abacus -- Remarks on winding numbers -- On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian -- Small perturbations of the automorphisms of the torus -- The classical theory of perturbations and the problem of stability of planetary systems -- Letter to the editor -- Dynamical systems and group representations at the Stockholm Mathematics Congress -- Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian -- Small denominators and stability problems in classical and celestial mechanics -- Small denominators and problems of stability of motion in classical and celestial mechanics -- Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region -- On a theorem of Liouville concerning integrable problems of dynamics -- Instability of dynamical systems with several degrees of freedom -- On the instability of dynamical systems with several degrees of freedom -- Errata to V.I. Arnol’d’s paper: “Small denominators. I.” -- Small denominators and the problem of stability in classical and celestial mechanics -- Stability and instability in classical mechanics -- Conditions for the applicability, and estimate of the error, of an averaging method for systems which pass through states of resonance in the course of their evolution -- On a topological property of globally canonical maps in classical mechanics En línea: http://dx.doi.org/10.1007/978-3-642-01742-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34068 Collected Works : Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965 [documento electrónico] / Vladimir I. Arnold ; SpringerLink (Online service) ; Givental, Alexander B ; Khesin, Boris A ; Marsden, Jerrold E ; Varchenko, Alexander N ; Vassiliev, Victor A ; Viro, Oleg Ya ; Zakalyukin, Vladimir M . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009 . - XIII, 487 p : online resource. - (Vladimir I. Arnold - Collected Works; 1) .
ISBN : 978-3-642-01742-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Partial differential equations Functions of real variables Physics Differential Equations Theoretical, Mathematical and Computational Real Clasificación: 51 Matemáticas Nota de contenido: On the representation of functions of two variables in the form ?[?(x) + ?(y)] -- On functions of three variables -- The mathematics workshop for schools at Moscow State University -- The school mathematics circle at Moscow State University: harmonic functions -- On the representation of functions of several variables as a superposition of functions of a smaller number of variables -- Representation of continuous functions of three variables by the superposition of continuous functions of two variables -- Some questions of approximation and representation of functions -- Kolmogorov seminar on selected questions of analysis -- On analytic maps of the circle onto itself -- Small denominators. I. Mapping of the circumference onto itself -- The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case -- Generation of almost periodic motion from a family of periodic motions -- Some remarks on flows of line elements and frames -- A test for nomographic representability using Decartes’ rectilinear abacus -- Remarks on winding numbers -- On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian -- Small perturbations of the automorphisms of the torus -- The classical theory of perturbations and the problem of stability of planetary systems -- Letter to the editor -- Dynamical systems and group representations at the Stockholm Mathematics Congress -- Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian -- Small denominators and stability problems in classical and celestial mechanics -- Small denominators and problems of stability of motion in classical and celestial mechanics -- Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region -- On a theorem of Liouville concerning integrable problems of dynamics -- Instability of dynamical systems with several degrees of freedom -- On the instability of dynamical systems with several degrees of freedom -- Errata to V.I. Arnol’d’s paper: “Small denominators. I.” -- Small denominators and the problem of stability in classical and celestial mechanics -- Stability and instability in classical mechanics -- Conditions for the applicability, and estimate of the error, of an averaging method for systems which pass through states of resonance in the course of their evolution -- On a topological property of globally canonical maps in classical mechanics En línea: http://dx.doi.org/10.1007/978-3-642-01742-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34068 Ejemplares
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Título : Mathematical Aspects of Classical and Celestial Mechanics : Third Edition Tipo de documento: documento electrónico Autores: Vladimir I. Arnold ; SpringerLink (Online service) ; Kozlov, Valery V ; Neishtadt, Anatoly I Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Encyclopaedia of Mathematical Sciences, ISSN 0938-0396 num. 3 Número de páginas: XIII, 505 p Il.: online resource ISBN/ISSN/DL: 978-3-540-48926-9 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Differential equations Partial differential Physics Dynamical Systems and Theory Theoretical, Mathematical Computational Ordinary Equations Clasificación: 51 Matemáticas Resumen: In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated Nota de contenido: Basic Principles of Classical Mechanics -- The n-Body Problem -- Symmetry Groups and Order Reduction -- Variational Principles and Methods -- Integrable Systems and Integration Methods -- Perturbation Theory for Integrable Systems -- Non-Integrable Systems -- Theory of Small Oscillations -- Tensor Invariants of Equations of Dynamics En línea: http://dx.doi.org/10.1007/978-3-540-48926-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35002 Mathematical Aspects of Classical and Celestial Mechanics : Third Edition [documento electrónico] / Vladimir I. Arnold ; SpringerLink (Online service) ; Kozlov, Valery V ; Neishtadt, Anatoly I . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XIII, 505 p : online resource. - (Encyclopaedia of Mathematical Sciences, ISSN 0938-0396; 3) .
ISBN : 978-3-540-48926-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Differential equations Partial differential Physics Dynamical Systems and Theory Theoretical, Mathematical Computational Ordinary Equations Clasificación: 51 Matemáticas Resumen: In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated Nota de contenido: Basic Principles of Classical Mechanics -- The n-Body Problem -- Symmetry Groups and Order Reduction -- Variational Principles and Methods -- Integrable Systems and Integration Methods -- Perturbation Theory for Integrable Systems -- Non-Integrable Systems -- Theory of Small Oscillations -- Tensor Invariants of Equations of Dynamics En línea: http://dx.doi.org/10.1007/978-3-540-48926-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35002 Ejemplares
Signatura Medio Ubicación Sección Estado ningún ejemplar Mathematical Events of the Twentieth Century / Bolibruch, A. A ; Osipov, Yu. S ; Sinai, Ya. G ; Vladimir I. Arnold ; Vershik, A. M ; Manin, Yu. I (2006)
Título : Mathematical Events of the Twentieth Century Tipo de documento: documento electrónico Autores: Bolibruch, A. A ; Osipov, Yu. S ; Sinai, Ya. G ; Vladimir I. Arnold ; Vershik, A. M ; Manin, Yu. I Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Número de páginas: VIII, 545 p. 96 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-29462-7 Idioma : Inglés (eng) Palabras clave: Mathematics History Physics of Mathematical Sciences Mathematics, general Physics, Clasificación: 51 Matemáticas Resumen: Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. The present collection is intended primarily to gather in one book the t- timonies of the participants in the development of mathematics over the past century. In their articles the authors have expressed their own points of view on the events that took place. The editors have not felt that they had a right to make any changes, other than stylistic ones, or to add any of their own commentary to the text. Naturally, the points of view of the authors should not be construed as those of the editors. The list of mathematicians invited to participate in the present edition was quite long. Unfortunately, some of the authors for various reasons did not accept our invitation, and regretfully a number of areas of research are not fully represented here. Nevertheless, the material that has been assembled is of great value not only in the scientific sense, but also in its historical context. We wish to express our gratitude to all the authors who contributed Nota de contenido: Dynamical Systems in the 1960s: The Hyperbolic Revolution -- From Hilbert’s Superposition Problem to Dynamical Systems -- Inverse Monodromy Problems of the Analytic Theory of Differential Equations -- What Modern Mathematical Physics Is Supposed to Be -- Discovery of the Maximum Principle -- The Qualitative Theory of Differential Equations in the Plane -- Computerization… Let’s Be Careful -- The Generalized Shift, Transformation Operators, and Inverse Problems -- Mathematics and the Trajectories of Typhoons -- Hilbert’s Tenth Problem: Diophantine Equations in the Twentieth Century -- Observations on the Movement of People and Ideas in Twentieth-Century Mathematics -- About Aleksandrov, Pontryagin and Their Scientific Schools -- Hilbert’s Seventh Problem -- The Great Kolmogorov -- Numbers as Functions: The Development of an Idea in the Moscow School of Algebraic Geometry -- The P NP-Problem: A View from the 1990s -- Homoclinic Trajectories: From Poincaré to the Present -- From “Disorder” to Nonlinear Filtering and Martingale Theory -- How Mathematicians and Physicists Found Each Other in the Theory of Dynamical Systems and in Statistical Mechanics -- Approximation Theory in the Twentieth Century -- The Life and Fate of Functional Analysis in the Twentieth Century -- Half a Century As One Day -- Nikolai Nikolaevich Bogolyubov — Mathematician by the Grace of God -- Global Solvability Versus Collapse in the Dynamics of an Incompressible Fluid En línea: http://dx.doi.org/10.1007/3-540-29462-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34922 Mathematical Events of the Twentieth Century [documento electrónico] / Bolibruch, A. A ; Osipov, Yu. S ; Sinai, Ya. G ; Vladimir I. Arnold ; Vershik, A. M ; Manin, Yu. I . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - VIII, 545 p. 96 illus : online resource.
ISBN : 978-3-540-29462-7
Idioma : Inglés (eng)
Palabras clave: Mathematics History Physics of Mathematical Sciences Mathematics, general Physics, Clasificación: 51 Matemáticas Resumen: Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. The present collection is intended primarily to gather in one book the t- timonies of the participants in the development of mathematics over the past century. In their articles the authors have expressed their own points of view on the events that took place. The editors have not felt that they had a right to make any changes, other than stylistic ones, or to add any of their own commentary to the text. Naturally, the points of view of the authors should not be construed as those of the editors. The list of mathematicians invited to participate in the present edition was quite long. Unfortunately, some of the authors for various reasons did not accept our invitation, and regretfully a number of areas of research are not fully represented here. Nevertheless, the material that has been assembled is of great value not only in the scientific sense, but also in its historical context. We wish to express our gratitude to all the authors who contributed Nota de contenido: Dynamical Systems in the 1960s: The Hyperbolic Revolution -- From Hilbert’s Superposition Problem to Dynamical Systems -- Inverse Monodromy Problems of the Analytic Theory of Differential Equations -- What Modern Mathematical Physics Is Supposed to Be -- Discovery of the Maximum Principle -- The Qualitative Theory of Differential Equations in the Plane -- Computerization… Let’s Be Careful -- The Generalized Shift, Transformation Operators, and Inverse Problems -- Mathematics and the Trajectories of Typhoons -- Hilbert’s Tenth Problem: Diophantine Equations in the Twentieth Century -- Observations on the Movement of People and Ideas in Twentieth-Century Mathematics -- About Aleksandrov, Pontryagin and Their Scientific Schools -- Hilbert’s Seventh Problem -- The Great Kolmogorov -- Numbers as Functions: The Development of an Idea in the Moscow School of Algebraic Geometry -- The P NP-Problem: A View from the 1990s -- Homoclinic Trajectories: From Poincaré to the Present -- From “Disorder” to Nonlinear Filtering and Martingale Theory -- How Mathematicians and Physicists Found Each Other in the Theory of Dynamical Systems and in Statistical Mechanics -- Approximation Theory in the Twentieth Century -- The Life and Fate of Functional Analysis in the Twentieth Century -- Half a Century As One Day -- Nikolai Nikolaevich Bogolyubov — Mathematician by the Grace of God -- Global Solvability Versus Collapse in the Dynamics of an Incompressible Fluid En línea: http://dx.doi.org/10.1007/3-540-29462-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34922 Ejemplares
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