An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings

Borin, Daniel; Livorati, André Luís Prando; Leonel, Edson Denis

doi:10.1016/j.chaos.2023.113965

Cited by 2 publications

(3 citation statements)

References 31 publications

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“…Essentially, if a system exhibits scaling invariance, its expected behaviors stay consistent regardless of scale. This characteristic is observed in diverse systems such as chaotic dynamics [26], human dynamics [39] and social networks [40].…”

Section: Scattering Properties: Scaling Invariance Of Survival Probab...mentioning

confidence: 93%

“…This probability refers to the possibility of a given particle remaining inside of a determined region after n interactions. Numerically, this measure is computed as [26]…”

Section: Scattering Properties: Scaling Invariance Of Survival Probab...mentioning

confidence: 99%

“…This probability quantifies the likelihood of a diffusing particle remaining within a specific region at a given point in time. In the context of fully chaotic systems, the behavior of survival probability exhibits a distinct pattern over time, characterized by exponential decay [26]. These properties have not been explored for Caputo fractional maps.…”

Section: Introductionmentioning

confidence: 99%

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Caputo fractional standard map: Scaling invariance analyses

Borin

2024

Chaos, Solitons & Fractals

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Section: Scattering Properties: Scaling Invariance Of Survival Probab...mentioning

confidence: 93%

“…This probability refers to the possibility of a given particle remaining inside of a determined region after n interactions. Numerically, this measure is computed as [26]…”

Section: Scattering Properties: Scaling Invariance Of Survival Probab...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Caputo fractional standard map: Scaling invariance analyses

Borin

2024

Chaos, Solitons & Fractals

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A Discrete Hamilton–Jacobi Theory for Contact Hamiltonian Dynamics

Esen,

Sardón,

Zajac

2024

Mathematics

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In this paper, we propose a discrete Hamilton–Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton–Jacobi theory for continuous contact Hamiltonian dynamics. Then, rooting on the discrete contact Lagrangian formulation, we obtain the discrete equations for Hamiltonian dynamics by the discrete Legendre transformation. Based on the discrete contact Hamilton equation, we construct a discrete Hamilton–Jacobi equation for contact Hamiltonian dynamics. We show how the discrete Hamilton–Jacobi equation is related to the continuous Hamilton–Jacobi theory presented in this work. Then, we propose geometric foundations of the discrete Hamilton–Jacobi equations on contact manifolds in terms of discrete contact flows. At the end of the paper, we provide a numerical example to test the theory.

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An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings

Cited by 2 publications

References 31 publications

Caputo fractional standard map: Scaling invariance analyses

Caputo fractional standard map: Scaling invariance analyses

A Discrete Hamilton–Jacobi Theory for Contact Hamiltonian Dynamics

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