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.
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.
From the reviews:
"In this book, the authors mainly study two kinds of problems. The first is the existence of nontrivial fixed points of Frobenius Perron operators, and the other concerns the computation of such fixed points. ... This book can be used as a textbook for students of pure mathematics, applied mathematics and computational mathematics as an introductory course of the ergodic theory of dynamical systems for the purpose of entering the related frontier of interdisciplinary areas." (Nasir N. Ganikhodjaev, Zentralblatt MATH, Vol. 1171, 2009)
