Statistical Properties of Deterministic Systems [electronic resource] / by Jiu Ding, Aihui Zhou.

By: Ding, Jiu [author.]
Contributor(s): Zhou, Aihui [author.] | SpringerLink (Online service)
Material type: TextTextSeries: Tsinghua University Texts: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: 270 p. 4 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540853671Subject(s): Mathematics | Operator theory | Applied mathematics | Engineering mathematics | Computer mathematics | Numerical analysis | Mathematics | Applications of Mathematics | Numerical Analysis | Operator Theory | Computational Mathematics and Numerical AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: T57-57.97Online resources: Click here to access online
Contents:
Foundations of Measure Theory -- Rudiments of Ergodic Theory -- Frobenius-Perron Operators -- Invariant Measures—Existence -- Invariant Measures—Computation -- Convergence Rate Analysis -- Entropy -- Applications of Invariant Measures.
In: Springer eBooksSummary: Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.
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Foundations of Measure Theory -- Rudiments of Ergodic Theory -- Frobenius-Perron Operators -- Invariant Measures—Existence -- Invariant Measures—Computation -- Convergence Rate Analysis -- Entropy -- Applications of Invariant Measures.

Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.

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