Partial barriers to chaotic transport in 4D symplectic maps

Chaotic transport in Hamiltonian systems is often restricted due to the presence of partial barriers, leading to a limited flux between different regions in phase phase. Typically, the most restrictive partial barrier in a 2D symplectic map is based on a cantorus, the Cantor set remnants of a broken...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Firmbach, Markus, Bäcker, Arnd, Ketzmerick, Roland
Format: Article
Language:English
Subjects:
Arnold diffusion
Diffusion barriers
Diffusion rate
Hamiltonian functions
Manifolds
Toruses
Online Access:Get full text
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Summary:Chaotic transport in Hamiltonian systems is often restricted due to the presence of partial barriers, leading to a limited flux between different regions in phase phase. Typically, the most restrictive partial barrier in a 2D symplectic map is based on a cantorus, the Cantor set remnants of a broken 1D torus. For a 4D symplectic map we establish a partial barrier based on what we call a cantorus-NHIM, a normally hyperbolic invariant manifold (NHIM) with the structure of a cantorus. Using a flux formula, we determine the global 4D flux across a partial barrier based on a cantorus-NHIM by approximating it with high-order periodic NHIMs. In addition, we introduce a local 3D flux depending on the position along a resonance channel, which is relevant in the presence of slow Arnold diffusion. Moreover, for a partial barrier composed of stable and unstable manifolds of a NHIM we utilize periodic NHIMs to quantify the corresponding flux.
ISSN:2331-8422
DOI:10.48550/arxiv.2210.09863