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. Contains both the theoretical analysis and the numerical analysis of the operator Fills the gap in the literature between theoretic ergodic theory and computational ergodic theory First textbook that incorporates numerical methodswith some topics of modern ergodic theory Both educational and research oriented Suitable as a graduate text and as reference book Exercises complete each chapter INDICE: Preface.- 1. Introduction.- 2. Foundations of Measure Theory.- 3. Rudiments of Ergodic Theory.- 4. Frobenius-Perron Operators.- 5. Absolutely Continuous Invariant Measures - Existence.- 6. Absolutely Continuous Invariant Measures- Computation.- 7. Convergence Rate Analysis.- 8. Entropy.- 9. Applications of Invariant Measures.
- ISBN: 978-3-540-85366-4
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 270
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés