Anomalous Diffusion: Deterministic and Stochastic Perspectives

Artuso, Roberto; Burioni, Raffaella

doi:10.1007/978-3-642-54251-0_10

Cited by 2 publications

(2 citation statements)

References 65 publications

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“…One of the most remarkable advances in modern dynamics lies in the recognition that deterministic systems may exhibit statistical properties typical of purely stochastic processes: for instance such systems may display diffusion properties similar to random walks [1][2][3][4]. Area-preserving maps (see for instance [1]) represent a prominent example of Hamiltonian systems where subtle features of dynamics, as integrability vs chaotic properties, may be studied.…”

Section: Introductionmentioning

confidence: 99%

Records and occupation time statistics for area-preserving maps

Artuso¹,

Oliveira²,

Manchein³

2023

Preprint

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Section: Introductionmentioning

confidence: 99%

Records and occupation time statistics for area-preserving maps

Artuso¹,

Oliveira²,

Manchein³

2023

Preprint

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show abstract

“…One of the most remarkable advances in modern dynamics lies in the recognition that deterministic systems may exhibit statistical properties typical of purely stochastic processes: for instance, such systems may display diffusion properties similar to random walks [1][2][3][4]. Area-preserving maps (see, for instance, [1]) represent a prominent example of Hamiltonian systems where subtle features of dynamics, such as integrability vs. chaotic properties, may be studied.…”

Section: Introductionmentioning

confidence: 99%

Records and Occupation Time Statistics for Area-Preserving Maps

Artuso

Oliveira

Manchein

2023

Entropy

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A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated with stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on 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. Our results confirm and expand known results for the standard map: when a chaotic sea is present, transport is diffusive, and records statistics and the fraction of occupation time in the positive half-axis reproduce the laws for simple symmetric random walks. In the case of the triangle map, we retrieve the previously observed anomalous transport, and we show that records statistics exhibit similar anomalies. When we investigate occupation time statistics and persistence probabilities, our numerical experiments are compatible with a generalized arcsine law and transient behavior of the dynamics.

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Anomalous Diffusion: Deterministic and Stochastic Perspectives

Cited by 2 publications

References 65 publications

Records and occupation time statistics for area-preserving maps

Records and occupation time statistics for area-preserving maps

Records and Occupation Time Statistics for Area-Preserving Maps

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