Dynamical systems : stability, symbolic dynamics, and chaos /
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 unders...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
CRC Press,
©1995.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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 HTnon 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. |
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| Physical Description: | 1 online resource (iii, 468 pages) : illustrations |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 451-462) and index. |
| ISBN: | 9780429161650 0429161654 |