Contractivity and ergodicity of the random map x →


Journal Article

The long time behavior of the random map xn → xn+1 = |xn-θn| is studied under various assumptions on the distribution of the θn. One of the interesting features of this random dynamical system is that for a single fixed deterministic θ the map is not a contraction, while the composition is almost surely a contraction if θ is chosen randomly with only mild assumptions on the distribution of the θ's. The system is useful as an explicit model where more abstract ideas can be explored concretely. We explore various measures of convergence rates, hyperbolically from randomness, and the structure of the random attractor.

Full Text

Duke Authors

Cited Authors

  • Mattingly, JC

Published Date

  • June 26, 2003

Published In

Volume / Issue

  • 47 / 2

Start / End Page

  • 333 - 343

International Standard Serial Number (ISSN)

  • 0040-585X

Digital Object Identifier (DOI)

  • 10.1137/S0040585X97979767

Citation Source

  • Scopus