Dynamical Systems: Stability, Symbolic Dynamics, and Chaos

ISBN-13: 9780849384950 / Angielski / Twarda / 1998 / 520 str.

R. Clark Robinson; J. C. Robinson;Robinson Clark

Opis

Several distinctive aspects make Dynamical Systems unique, including:
treating the subject from a mathematical perspective with the proofs of most of the results included
providing a careful review of background materials
introducing ideas through examples and at a level accessible to a beginning graduate student
focusing on multidimensional systems of real variables
The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.

Recenzje

"...was impressed with the teachability of this text and with the exercises at the end of each chapter, which seemed be nicely graded in difficulty."
-D. Givoli, APPLIED MECHANICS REVIEWS

Spis treści

Introduction
One Dimensional Dynamics by Iteration
Chaos and Its Measurement
Linear Systems
Analysis near Fixed Points and Periodic Orbits
Hamiltonian Systems
Bifurcation of Periodic Points
Examples of Hyperbolic Sets and Attractors
Measurement of Chaos in Higher Dimensions
Global Theory of Hyperbolic Systems
Generic Properties
Smoothness of Stable Manifolds and Applications

O autorze

Clark Robinson