Exotic Attractors

From Liapunov Stability to Riddled Basins

Jorge Buescu (Autor)

Buch | Softcover

XIV, 130 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 1997
Springer Basel (Verlag)
978-3-0348-7423-6 (ISBN)

Artikel merken

This book grew out of the work developed at the University of Warwick, under the supervision of Ian Stewart, which formed the core of my Ph.D. Thesis. Most of the results described were obtained in joint work with Ian; as usual under these circumstances, many have been published in research journals over the last two years. Part of Chapter 3 was also joint work with Peter Ashwin. I would like to stress that these were true collaborations. We worked together at all stages; it is meaningless to try to identify which idea originated from whom. While preparing this book, however, I felt that a mere description of the results would not be fitting. First of all, a book is aimed at a wider audience than papers in research journals. More importantly, the work should assume as little as possible, and it should be brought to a form which is pleasurable, not painful, to read.

1 Attractors in Dynamical Systems.- 1.1 Introduction.- 1.2 Basic definitions.- 1.3 Topological and dynamical consequences.- 1.4 Attractors.- 1.5 Examples and counterexamples.- 1.6 Historical remarks and further comments.- 2 Liapunov Stability and Adding Machines.- 2.1 Introduction.- 2.2 Adding Machines and Denjoy maps.- 2.3 Stable Cantor sets are Adding Machines.- 2.4 Adding Machines and periodic points: interval maps.- 2.5 Interlude: Adding Machines as inverse limits.- 2.6 Stable ?-limit sets are Adding Machines.- 2.7 Classification of Adding Machines.- 2.8 Existence of Stable Adding Machines.- 2.9 Historical remarks and further comments.- 3 From Attractor to Chaotic Saddle: a journey through transverse instability.- 3.1 Introduction.- 3.2 Normal Liapunov exponents and stability indices.- 3.3 Normal parameters and normal stability.- 3.4 Example: ?2-symmetric maps on ?2.- 3.5 Example: synchronization of coupled systems.- 3.6 Historical remarks and further comments.

"The author gives a thorough insight into topological and ergodic properties of invariant subsets and their structure, classifies the main concepts which are used in the book and describes their characteristics. In addition, some new important concepts which, for the most part, have been previously known only from articles are presented...
The manner of exposition is in the tradition of mathematics: rigorous description of the concepts and notions of attractors in dynamics, and detailed proofs of main results. At the same time, the material is presented at an acceptable level for the wide circle of researchers and post-graduate students who apply ideas of dynamical systems. Moreover, because the book is self-contained, readers can use it as a fine introduction to the modern theory of attractors and related topics.
The book is clearly written, and it has many references (about 120 entries); in addition, some results are supported by helpful examples (and even sometimes counterexamples). Moreover, at the end of each chapter the readers can find very useful general comments and historical remarks."
-- Mathematical Reviews

Erscheint lt. Verlag	18.4.2012
Reihe/Serie	Progress in Mathematics
Zusatzinfo	XIV, 130 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	234 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Chaos • Dynamical Systems • Dynamics • ergodic theory • instability • stability • Stress
ISBN-10	3-0348-7423-5 / 3034874235
ISBN-13	978-3-0348-7423-6 / 9783034874236
Zustand	Neuware