Navigate MathSciNet Jump to Search or Browse Screens Item: 11 of 17 Return to headlines First Previous Next Last MSN-Support Help Select alternative format: BibTeX ASCII MR1709869 (2000f:37069) Froyland, Gary (D-PDRB) Ulam’s method for random interval maps. (English summary) Nonlinearity 12 (1999), no. 4, 1029–1052. 37H99 (28D05 34E05 37A25 37A50) References: 19 Reference Citations: 2 Review Citations: 1 The author considers a dynamical system defined by random compositions of piecewise expand- ing maps of an interval [see S. Pelikan, Trans. Amer. Math. Soc. 281 (1984), no. 2, 813–825; MR0722776 (85i:58070) ]. Two models of controlling the compositions are considered: the classi- cal i.i.d. model and a new Markov model. For both cases, the author develops precise estimates on the speed of convergence of the iterates of the Perron-Frobenius operator. Then, he uses Ulam’s method of approximating the P-F operator by finite-dimensional operators (matrices) and proves the convergence of the approximations. Again, precise estimates of the speed of convergence are given. Reviewed by Pawel Gora [References] Note: This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors. 1. Boyarsky A and Lou Y S 1992 Existence of absolutely continuous invariant measures for higher dimensional random maps Dyn. Stab. Syst. 7 233–44 MR1232960 (94g:58119) 2. Ding J and Zhou A 1996 Finite approximations of Frobenius-Perron operators. A solution of Ulam’s conjecture to multi-dimensional transformations Physica D 92 61–8 MR1384679 (97a:58097) 3. Froyland G 1998 Approximating physical invariant measures of mixing dynamical sys- tems in higher dimensions Nonlinear Anal. Theory Methods Appl. 32 831–60 MR1618409 (99d:58105)