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- W4287018855 abstract "Let $Theta$ be a finite alphabet. We consider a bundle of measure preserving transformations $(T_{theta})_{theta in Theta}$ acting on a probability space $(X,mu)$, which are chosen randomly according to an ergodic stochastic process $(Xi,nu,sigma)$ with state space $Theta$. This describes a paradigmatic case of a random dynamical system (RDS). Considering a finite partition $mathcal{P}$ of $X$ we show that the conditional algorithmic complexity of a random orbit $x, T_{alpha_{0}}(x),T_{alpha_{1}}circ T_{alpha_{0}}(x),...$ in $X$ along a sequence $alpha = alpha_{0}alpha_{1}alpha_{2}...$ in $Xi$ equals almost surely the fiber entropy of the RDS with respect to $mathcal{P}$, whenever the latter is ergodic. This extends a classical result of A. A. Brudno connecting algorithmic complexity and entropy in deterministic dynamical systems." @default.
- W4287018855 created "2022-07-25" @default.
- W4287018855 creator A5087440349 @default.
- W4287018855 date "2021-08-30" @default.
- W4287018855 modified "2023-09-26" @default.
- W4287018855 title "Fiber entropy and algorithmic complexity of random orbits" @default.
- W4287018855 doi "https://doi.org/10.48550/arxiv.2108.13019" @default.
- W4287018855 hasPublicationYear "2021" @default.
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