Finite Approximations of Frobenius-Perron Operators. A Solution of Ulam's Conjecture to Multi-Dimensional Transformations

Authors

Jiu Ding, University of Southern MississippiFollow
Aihui Zhou, Academia SinicaFollow

Document Type

Article

Publication Date

4-15-1996

Department

Physics and Astronomy

School

Mathematics and Natural Sciences

Abstract

We prove that Ulam's piecewise constant approximation algorithm is convergent for computing an absolutely continuous invariant measure associated with a piecewise C² expanding transformation or a Jablonski transformation S: [0, 1]^N ⊂ R^N → [0, 1]^N. This solves an extension of Ulam's conjecture to multi-dimensions and generalizes the convergence result given by T.-Y. Li for one-dimensional transformations.

Publication Title

Physica D: Nonlinear Phenomena

Volume

92

Issue

1-2

First Page

61

Last Page

68

Recommended Citation

Ding, J., Zhou, A. (1996). Finite Approximations of Frobenius-Perron Operators. A Solution of Ulam's Conjecture to Multi-Dimensional Transformations. Physica D: Nonlinear Phenomena, 92(1-2), 61-68.
Available at: https://aquila.usm.edu/fac_pubs/5569