A first course in dynamics

With a panorama of recent developments

Boris Hasselblatt, Anatole Katok

434 pages, parution le 08/09/2003

Ajouter à une liste

Indisponible

Résumé

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course.

The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

Introduction

A course in dynamics : From simple to complicated behavior
- Systems with stable asymptotic behavior
- Linear maps and linear differential equations
- Recurrence and equidistribution on the circle
- Recurrence and equidistribution in higher dimension
- Conversative systems
- Simple systems with complicated orbit structure
- Entropy and chaos

Panorama of dynamical systems
- Simple dynamics as o tool
- Hyperbolic dynamics
- Quadratic maps
- Homoclinic tangles
- Strange attractors
- Strange attractors
- Variational methods, twist maps, and closed geodesics
- Dynamics, number theory, and diophantine approximation

Reading
Appendix
Hints and answers
Solutions
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Boris Hasselblatt, Anatole Katok
Parution	08/09/2003
Nb. de pages	434
Format	17,5 x 25,3
Couverture	Broché
Poids	755g
Intérieur	Noir et Blanc
EAN13	9780521587501
ISBN13	978-0-521-58750-1