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Publications [#243846] of Jonathan C. Mattingly

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Papers Published

  1. Mattingly, JC, Contractivity and ergodicity of the random map $x\mapsto\vert x-θ\vert $, Rossi\u\i skaya Akademiya Nauk. Teoriya Veroyatnoste\u\i i ee Primeneniya, vol. 47 no. 2 (2002), pp. 388-397, Society for Industrial & Applied Mathematics (SIAM), ISSN 0040-585X [repository], [doi]
    (last updated on 2024/03/28)

    Abstract:
    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.

 

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