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arXiv · 2301.03577

Records and occupation time statistics for area-preserving maps

Roberto Artuso·Tulio M. de Oliveira·Cesar Manchein
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Abstract

A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on a non-compact phase space. We consider here two examples of area-preserving maps: the Chirikov-Taylor standard map and the Casati-Prosen triangle map, and we investigate transport properties, records' statistics and occupation time statistics. While the standard map, when a chaotic sea is present, always reproduces results expected for simple random walks, the triangle map -- whose analysis still displays many elusive points -- behaves in a wildly different way, some of the features being compatible with a transient (non conservative) nature of the dynamics.

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Roberto Artuso, Tulio M. de Oliveira, Cesar Manchein. 2023-01-09. Records and occupation time statistics for area-preserving maps. https://doi.org/10.3390/e25020269

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