The Theory of Chaotic Attractors (eBook, PDF)

Redaktion: Hunt, Brian R.; Nusse, Helena E.; Li, Tien-Yien; Kennedy, Judy A.

• Format: PDF

Produktbeschreibung

This volume contains a selection of key papers in the theory of chaotic attractors over the past 40 years, and is dedicated to James Yorke on the occasion of his 60th birthday. It includes an introduction to the theory of chaotic attractors and an overview of Yorke's pioneering work in the field.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 514
• Erscheinungstermin: 5. Juni 2013
• Englisch
• ISBN-13: 9780387218304
• Artikelnr.: 44177969

Inhaltsangabe

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 Piecewise Hyperbolic Maps.- Ergodic Theory of Chaos and Strange Attractors.- Another Proof of Jakobson's Theorem and Related Results.- Unstable Periodic Orbits and the Dimensions of Multifractal Chaotic Attractors.- Absolutely Continuous Invariant Measures for Piecewise Expanding C2 Transformation in RN.- 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.

Rezensionen

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)