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TitleThe Theory of Chaotic Attractors [electronic resource] / edited by Brian R. Hunt, Tien-Yien Li, Judy A. Kennedy, Helena E. Nusse
ImprintNew York, NY : Springer New York : Imprint: Springer, 2004
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Descript X, 514 p. online resource


The development of the theory of chaotic dynamics and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. This volume collects several of the most influential papers in chaos theory from the past 40 years, starting with Lorenz's seminal 1963 article and containing classic papers by Lasota and Yorke (1973), Bowen and Ruelle (1975), Li and Yorke (1975), May (1976), Henon (1976), Milnor (1985), Eckmann and Ruelle (1985), Grebogi, Ott, and Yorke (1988), Benedicks and Young (1993) and many others, with an emphasis on invariant measures for chaotic systems. Dedicated to Professor James Yorke, a pioneer in the field and a recipient of the 2003 Japan Prize, the book includes an extensive, anecdotal introduction discussing Yorke's contributions and giving readers a general overview of the key developments of the theory from a historical perspective


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 Jakobsonโ{128}{153}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

Mathematics Dynamics Ergodic theory Mathematics Dynamical Systems and Ergodic Theory


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