Firmbach M, Bäcker A, Ketzmerick R. Partial barriers to chaotic transport in 4D symplectic maps.
CHAOS (WOODBURY, N.Y.) 2023;
33:013125. [PMID:
36725645 DOI:
10.1063/5.0130682]
[Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/12/2022] [Indexed: 06/18/2023]
Abstract
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.
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