Partial barriers to chaotic transport in 4D symplectic maps

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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 space. 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 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.


Original languageEnglish
Article number013125
Number of pages18
Issue number1
Publication statusPublished - Jan 2023

External IDs

WOS 000917936100003



  • Arnold diffusion, Frequency-analysis, Global dynamics, Hamiltonian-systems, Hyperbolic invariant-manifolds, Instability, Multidimensional systems, Phase-space, Resonances, Tori

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