The Theory of Chaotic Attractors
(Sprache: Englisch)
The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting,...
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Klappentext zu „The Theory of Chaotic Attractors “
The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) fromSpringer Verlag in New York for their efforts in publishing this book.
This volume contains a selection of the most important papers in the theory of chaotic attractors over the past 40 years. It is dedicated to James Yorke - a pioneer in the field and a recipient of the 2003 Japan prize - on the occasion of his 60th birthday. The volume includes an introduction to Yorke's work and an overview of key developments in the theory of chaotic attractors.
Inhaltsverzeichnis zu „The Theory of Chaotic Attractors “
- Preface- Introduction
- Deterministic nonperiodic flow
- On invariant measures for expanding differentiable mappings
- On the existence of invariant measures for piecewise monotonic transformations
- The ergodic theory of Axiom A flows
- Period three implies chaos
- Simple mathematical models with very complicated dynamics
- A two-dimensional mapping with a strange attractor
- Strange attractors and chaotic motions of dynamical systems
- Ergodic properties of invariant measures for piecewise monotonic transformations
- The dimension of chaotic attractors
- Measuring the strangeness of strange attractors
- Invariant measures and variational principle for Lozi applications
- Ergodic properties of the Lozi mappings
- On the Concept of Attractor
- Bowen-Ruelle Measures for certain Piewise Hyperbolic Maps
- Ergodic Theory of Chaos and Strange Attractors
- Another Proof of Jakobson Theorem and Related Results
- Unstable periodic Orbits and the Dimensions of Multifractal Chaotic Attractors
- Absolutely Continuous Invariant Measures for Piecewise Expanding C Transformation in R
- Sinai-Bowen-Ruelle Measures for Certain Henon Maps
- On the Approximation of Complicated Dynamical Behavior
- Absolutely Continuous Invariant Measures for Piecewise Real-Analytic Expanding Maps on the Plane
- SRB Measures for Partially Hyperbolic Systems Whose Central Direction is Mostly Expanding
- SLYRB Measures: Natural Invariant Measures for Chaotic Systems
- Credits
Bibliographische Angaben
- 2004, 514 Seiten, Maße: 25,4 cm, Gebunden, Englisch
- Ed. by Brian R. Hunt, Judy A. Kennedy, Tien-Yien Li et al.
- Verlag: Springer Berlin
- ISBN-10: 0387403493
- ISBN-13: 9780387403496
Sprache:
Englisch
Rezension zu „The Theory of Chaotic Attractors “
From the reviews:"This book is a collection, from the last 40 years, of the most influential papers in the development of chaos theory. ... The editors are eminent in this field ... . Their selection of papers is excellent ... . it is a book for mathematics graduates specializing in non-linear dynamics. ... is a well-presented and well-deserved tribute to the life's work of Professor Yorke ... . might well be as that benchmark that mathematicians of the future will view its publication hundreds of years from now." (Dennis Morris, The Mathematical Gazette, March, 2005)
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