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About Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed. (Texts in Applied Mathematics 2)
<p>This edition contains a significant amount of new material. The main rea-</p><p>son for this is that the subject of applied dynamical systems theory has</p><p>seen explosive growth and expansion throughout the 1990s. Consequently,</p><p>a student needs a much larger toolbox today in order to begin research on</p><p>significant problems.</p><p>I also try to emphasize a broader and more unified point of view. My</p><p>goal is to treat dissipative and conservative dynamics, discrete and con-</p><p>tinuous time systems, and local and global behavior, as much as possible,</p><p>on the same footing. Many textbooks tend to treat most of these issues</p><p>separately (e.g., dissipative, discrete time, local dynamics; global dynamics</p><p>of continuous time conservative systems, etc.). However, in research one</p><p>generally needs to have an understanding of each of these areas, and their</p><p>inter-relations. For example, in studying a conservative continuous time</p><p>system, one might study periodic orbits and their stability by passing to a</p><p>Poincar´ e map (discrete time). The question of how stability may be affected</p><p>by dissipative perturbations may naturally arise. Passage to the Poincar´ e</p><p>map renders the study of periodic orbits a local problem (i.e., they are fixed</p><p>points of the Poincar´ e map), but their manifestation in the continuous time</p><p>problem may have global implications. An ability to put together a “big</p><p>picture” from many (seemingly) disparate pieces of information is crucial</p><p>for the successful analysis of nonlinear dynamical systems.</p><p>This edition has seen a major restructuring with respect to the first</p><p>edition in terms of the organization of the chapters into smaller units with</p><p>a single, common theme, and the exercises relevant to each chapter now</p><p>being given at the end of the respective chapter.</p><p>The bulk of the material in this book can be covered in three ten week</p><p>terms. This is an ambitious program, and requires relegating some of the</p><p>material to background reading (described below). My goal was to have the</p><p>necessary background material side-by-side with the material that I would</p><p>lecture on. This tends to be more demanding on the student, but with the</p><p>right guidance, it also tends to be more rewarding and lead to a deeper</p><p>understanding and appreciation of the subject.</p><p>The mathematical prerequisites for the course are really not great; ele-</p><p>mentary analysis, multivariable calculus, and linear algebra are sufficient.</p><p>In reality, this may not be enough on its own. A successful understanding</p><p>of applied dynamical systems theory requires the students to have an inte</p>
Detailed Information
| Author: | Stephen Wiggins |
|---|---|
| Publication Year: | 2003 |
| ISBN: | 387001778 |
| Pages: | 865 |
| Language: | other |
| File Size: | 5.4492 |
| Format: | |
| Price: | FREE |
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