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