| Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippii Dr. Aihni Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences... .. << 查看详细 |
| chapter 1 introduction 1.1 discrete deterministic systems—from order to chaos 1.2 statistical study of chaos exercises chapter 2 foundations of measure theory 2.1 measures and integration 2.2 basic integration theory 2.3 functions of bounded variation in one variable 2.4 functions of bounded variation in several variables 2.5 compactness and quasi—compactness 2.5.1 strong and wleak compactness 2.5.2 quasi-compactness exercises chapter 3 rudiments of ergodic theory 3.1 measure preserving transfcirmations 3.2 ergodicity,mixing and exactness 3.2.1 ergodicity 3.2.2 mixing and exactness 3.3 ergodic theorems 3.4 topological dynamical systems . exercises chapter 4 frobenius-perron operators 4.1 markov operatorst 4.2 nobenius—perron operators 4.3 koopman 0peratorst 4.4 ergodicity and frobenius—perron operators 4.5 decomposition theorem and spectral analysis exercises chapter 5 invariant measures——existence 5.1 general existence results 5.2 piecewise stretching mappings 5.3 piecewise convex mappings 5.4 piecewise expanding transformations exercises. chapter 6 invariant measures--computation 61 ulam’s method for one—dimensional mappings 6.2 ulam’s method for n—dimensional transformations 6.3 the markov method for one—dimensional mappings 6.4 the markov metho(~for n—dimensional transformations exercises- chapter 7 convergence rate analysis 7.1 error estimates for ulam’s method. 7.2 more explicit error estimates 7.3 error estimates for the markov method exercises chapter 8 entropy 8.1 shannon entropy 8.2 kolmogorov entropy 8.3 topological entropy 8.4 boltzmann entropy 8.5 boltzmann entropy and frobenius—perron operators exercises chapter 9 applications of invariant measures 9.1 decay of correlations 9.2 random number generationi 9.3 conformational dynamics of bio—molecules4： 9.4 ds—cdma in wireless communications exercises bibliography index |
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