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Título : Ergodic Theory, Hyperbolic Dynamics and Dimension Theory Tipo de documento: documento electrónico Autores: Luis Barreira ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2012 Colección: Universitext, ISSN 0172-5939 Número de páginas: XII, 290 p. 34 illus Il.: online resource ISBN/ISSN/DL: 978-3-642-28090-0 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Dynamical Systems and Theory Clasificación: 51 Matemáticas Resumen: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs Nota de contenido: Preface -- I Ergodic Theory -- 1.Basic Notions and Examples -- 2.Further Topics -- II Entropy and Pressure -- 3.Metric Entropy and Topological Entropy -- 4.Thermodynamic Formalism. III Hyperbolic Dynamics -- 5.Basic Notions and Examples -- 6.Invariant Manifolds and Markov Partitions -- IV Dimension Theory -- 7.Basic Notions and Examples -- 8.Dimension Theory of Hyperbolic Dynamics -- A Notions from Measure Theory -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-28090-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32971 Ergodic Theory, Hyperbolic Dynamics and Dimension Theory [documento electrónico] / Luis Barreira ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2012 . - XII, 290 p. 34 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-3-642-28090-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Dynamical Systems and Theory Clasificación: 51 Matemáticas Resumen: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs Nota de contenido: Preface -- I Ergodic Theory -- 1.Basic Notions and Examples -- 2.Further Topics -- II Entropy and Pressure -- 3.Metric Entropy and Topological Entropy -- 4.Thermodynamic Formalism. III Hyperbolic Dynamics -- 5.Basic Notions and Examples -- 6.Invariant Manifolds and Markov Partitions -- IV Dimension Theory -- 7.Basic Notions and Examples -- 8.Dimension Theory of Hyperbolic Dynamics -- A Notions from Measure Theory -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-28090-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32971 Ejemplares
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Título : Ergodic Theory : with a view towards Number Theory Tipo de documento: documento electrónico Autores: Einsiedler, Manfred ; SpringerLink (Online service) ; Ward, Thomas Editorial: London : Springer London Fecha de publicación: 2011 Otro editor: Imprint: Springer Número de páginas: XVII, 481 p Il.: online resource ISBN/ISSN/DL: 978-0-85729-021-2 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Measure Number Dynamical Systems and Theory Integration Clasificación: 51 Matemáticas Resumen: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory Nota de contenido: Motivation -- Ergodicity, Recurrence and Mixing -- Continued Fractions -- Invariant Measures for Continuous Maps -- Conditional Measures and Algebras -- Factors and Joinings -- Furstenberg’s Proof of Szemeredi’s Theorem -- Actions of Locally Compact Groups -- Geodesic Flow on Quotients of the Hyperbolic Plane -- Nilrotation -- More Dynamics on Quotients of the Hyperbolic Plane -- Appendix A: Measure Theory -- Appendix B: Functional Analysis -- Appendix C: Topological Groups En línea: http://dx.doi.org/10.1007/978-0-85729-021-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33114 Ergodic Theory : with a view towards Number Theory [documento electrónico] / Einsiedler, Manfred ; SpringerLink (Online service) ; Ward, Thomas . - London : Springer London : Imprint: Springer, 2011 . - XVII, 481 p : online resource.
ISBN : 978-0-85729-021-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Measure Number Dynamical Systems and Theory Integration Clasificación: 51 Matemáticas Resumen: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory Nota de contenido: Motivation -- Ergodicity, Recurrence and Mixing -- Continued Fractions -- Invariant Measures for Continuous Maps -- Conditional Measures and Algebras -- Factors and Joinings -- Furstenberg’s Proof of Szemeredi’s Theorem -- Actions of Locally Compact Groups -- Geodesic Flow on Quotients of the Hyperbolic Plane -- Nilrotation -- More Dynamics on Quotients of the Hyperbolic Plane -- Appendix A: Measure Theory -- Appendix B: Functional Analysis -- Appendix C: Topological Groups En línea: http://dx.doi.org/10.1007/978-0-85729-021-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33114 Ejemplares
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Título : Computational Ergodic Theory Tipo de documento: documento electrónico Autores: Choe, Geon Ho ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 13 Número de páginas: XX, 453 p. 250 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-27305-9 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Physics Applied mathematics Engineering Dynamical Systems and Theory Theoretical, Mathematical Computational Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society Nota de contenido: Prerequisites -- Invariant Measures -- The Birkhoff Ergodic Theorem -- The Central Limit Theorem -- More on Ergodicity -- Homeomorphisms of the Circle -- Mod 2 Uniform Distribution -- Entropy -- The Lyapunov Exponent: One-Dimensional Case -- The Lyapunov Exponent: Multidimensional Case -- Stable and Unstable Manifolds -- Recurrence and Entropy -- Recurrence and Dimension -- Data Compression En línea: http://dx.doi.org/10.1007/b138894 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35275 Computational Ergodic Theory [documento electrónico] / Choe, Geon Ho ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XX, 453 p. 250 illus : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 13) .
ISBN : 978-3-540-27305-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Physics Applied mathematics Engineering Dynamical Systems and Theory Theoretical, Mathematical Computational Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society Nota de contenido: Prerequisites -- Invariant Measures -- The Birkhoff Ergodic Theorem -- The Central Limit Theorem -- More on Ergodicity -- Homeomorphisms of the Circle -- Mod 2 Uniform Distribution -- Entropy -- The Lyapunov Exponent: One-Dimensional Case -- The Lyapunov Exponent: Multidimensional Case -- Stable and Unstable Manifolds -- Recurrence and Entropy -- Recurrence and Dimension -- Data Compression En línea: http://dx.doi.org/10.1007/b138894 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35275 Ejemplares
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Título : Mathematics of Complexity and Dynamical Systems Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Meyers, Robert A Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Número de páginas: 489 illus., 140 illus. in color. eReference Il.: online resource ISBN/ISSN/DL: 978-1-4614-1806-1 Idioma : Inglés (eng) Palabras clave: Mathematics Computer simulation Dynamics Ergodic theory Differential equations System Statistical physics Dynamical systems Complex Systems Simulation and Modeling Theory Physics, Complexity Theory, Control Ordinary Equations Clasificación: 51 Matemáticas Resumen: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifracticals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers Nota de contenido: Ergodic Theory -- Three Editor-in-Chief Selections: Catastrophe Theory; Infinite Dimensional Controllability; Philosophy of Science, Mathematical Models In.- Fractals and Multifractals -- Non-linear Ordinary Differential Equations and Dynamical Systems -- Non-Linear Partial Differential Equations -- Perturbation Theory -- Solitons -- Systems and Control Theory En línea: http://dx.doi.org/10.1007/978-1-4614-1806-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33238 Mathematics of Complexity and Dynamical Systems [documento electrónico] / SpringerLink (Online service) ; Meyers, Robert A . - New York, NY : Springer New York : Imprint: Springer, 2011 . - 489 illus., 140 illus. in color. eReference : online resource.
ISBN : 978-1-4614-1806-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer simulation Dynamics Ergodic theory Differential equations System Statistical physics Dynamical systems Complex Systems Simulation and Modeling Theory Physics, Complexity Theory, Control Ordinary Equations Clasificación: 51 Matemáticas Resumen: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifracticals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers Nota de contenido: Ergodic Theory -- Three Editor-in-Chief Selections: Catastrophe Theory; Infinite Dimensional Controllability; Philosophy of Science, Mathematical Models In.- Fractals and Multifractals -- Non-linear Ordinary Differential Equations and Dynamical Systems -- Non-Linear Partial Differential Equations -- Perturbation Theory -- Solitons -- Systems and Control Theory En línea: http://dx.doi.org/10.1007/978-1-4614-1806-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33238 Ejemplares
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Título : Dynamical Systems : An Introduction Tipo de documento: documento electrónico Autores: Luis Barreira ; SpringerLink (Online service) ; Valls, Claudia Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: IX, 209 p. 44 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-4835-7 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Global analysis (Mathematics) Manifolds Differential equations Hyperbolic geometry Dynamical Systems and Theory Analysis on Ordinary Equations Geometry Clasificación: 51 Matemáticas Resumen: The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics Nota de contenido: Introduction -- Basic Notions and Examples -- Topological Dynamics -- Low-Dimensional Dynamics -- Hyperbolic Dynamics I -- Hyperbolic Dynamics II -- Symbolic Dynamics -- Ergodic Theory En línea: http://dx.doi.org/10.1007/978-1-4471-4835-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32197 Dynamical Systems : An Introduction [documento electrónico] / Luis Barreira ; SpringerLink (Online service) ; Valls, Claudia . - London : Springer London : Imprint: Springer, 2013 . - IX, 209 p. 44 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-4835-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Global analysis (Mathematics) Manifolds Differential equations Hyperbolic geometry Dynamical Systems and Theory Analysis on Ordinary Equations Geometry Clasificación: 51 Matemáticas Resumen: The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics Nota de contenido: Introduction -- Basic Notions and Examples -- Topological Dynamics -- Low-Dimensional Dynamics -- Hyperbolic Dynamics I -- Hyperbolic Dynamics II -- Symbolic Dynamics -- Ergodic Theory En línea: http://dx.doi.org/10.1007/978-1-4471-4835-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32197 Ejemplares
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