© 1997
Laws of Chaos
Invariant Measures and Dynamical Systems in One Dimension
- 145 Citations
- 6.8k Downloads
Part of the Probability and Its Applications book series (PA)
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© 1997
Part of the Probability and Its Applications book series (PA)
"Well written with ample examples and exercises… It fills an important gap in the literature."
—Journal of the Indian Inst. of Science
"The book provides a personal view on invariant measures and dynamical systems in one dimension. It is given a detailed study of the piecewise linear transformations under another spirit than that of {W. Doeblin} developed in the commemorative volume [Doeblin and modern probability. Proceedings of the Doeblin conference "50 years after Doeblin: Developments in the theory of Markov chains, Markov processes and sums of independent random variables'', Contemporary Mathematics 149 (1993; articles are reviewed individually in Zbl )]. The book contains 13 chapters. Some titles are as follows: Spectral decomposition of the Frobenius-Perron operator, Markov transformations, Compactness theorem and Approximation of invariant densities, Stability of invariant measures, The inverse problem for the Frobenius-Perron equation and others. The style of the book is clear with good didactical perspectives for those who wish to study dynamical systems in connection with measure theory and ergodic theory. Finally, the book is a valuable contribution to the topic of Dynamical Systems."
—Zentralblatt Math