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- W4291336639 abstract "We study the effects of IID random perturbations of amplitude $epsilon > 0$ on the asymptotic dynamics of one-parameter families ${f_a : S^1 to S^1, a in [0,1]}$ of smooth multimodal maps which predominantly expanding, i.e., $|f'_a| gg 1$ away from small neighborhoods of the critical set ${ f'_a = 0 }$. We obtain, for any $epsilon > 0$, a emph{checkable, finite-time} criterion on the parameter $a$ for random perturbations of the map $f_a$ to exhibit (i) a unique stationary measure, and (ii) a positive Lyapunov exponent comparable to $int_{S^1} log |f_a'| , dx$. This stands in contrast with the situation for the deterministic dynamics of $f_a$, the chaotic regimes of which are determined by typically uncheckable, infinite-time conditions. Moreover, our finite-time criterion depends on only $k sim log (epsilon^{-1})$ iterates of the deterministic dynamics of $f_a$, which grows quite slowly as $epsilon to 0$." @default.
- W4291336639 created "2022-08-15" @default.
- W4291336639 creator A5021171630 @default.
- W4291336639 creator A5035343733 @default.
- W4291336639 date "2018-05-23" @default.
- W4291336639 modified "2023-09-28" @default.
- W4291336639 title "Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps" @default.
- W4291336639 doi "https://doi.org/10.48550/arxiv.1805.09219" @default.
- W4291336639 hasPublicationYear "2018" @default.
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