Dynamical SystemsStability, Symbolic Dynamics, and Chaos: Stability, Symbolic Dynamics, and Chaos (Studies in Advanced Mathematics) - Hardcover

Robinson, Clark

Hardcover

ISBN 10: 0849384931 ISBN 13: 9780849384936

Publisher: CRC Press, 1994

Synopsis

This new text/reference treats dynamical systems from a mathematical perspective, centering on multidimensional systems of real variables. Background material is carefully reviewed as it is used throughout the book, and ideas are introduced through examples. Numerous exercises help the reader understand presented theorems and master the techniques of the proofs and topic under consideration. 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. A proof of the existence and continuity of solutions with respect to initial conditions is included. Explicit formulas for the various bifurcations are included, and a treatment of the Hénon map and the Melnikov method is provided. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. Even the more local theory which is treated deals with characterizing types of solutions under various hypothesis. Later chapters deal more directly with more global aspects, with one chapter discussing various examples and later chapters giving the global theory.

About this title

Review

"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

Synopsis

A complete study of dynamical systems theory which focuses on the dynamics of both iteration of functions and solutions of ordinary differential equations. Symbolic dynamics, structural dynamics and chaos are the main ideas expressed in the book through examples of function and differential equations. Many low-level examples are also included to help the reader learn the meaning of the theorems and master the techniques of the proofs and topics under consideration. The text is intended for students and professionals in mathematics, physics and mechanical engineering.

Edition details

• Publisher: CRC Press
• Publication date: 1994
• Language: English
• ISBN 10: 0849384931
• ISBN 13: 9780849384936
• Binding: Hardcover
• Edition number: 1
• Number of pages: 480