Partial barriers to chaotic transport in 4D symplectic maps
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.
- Publication:
-
Chaos
- Pub Date:
- January 2023
- DOI:
- 10.1063/5.0130682
- arXiv:
- arXiv:2210.09863
- Bibcode:
- 2023Chaos..33a3125F
- Keywords:
-
- Nonlinear Sciences - Chaotic Dynamics;
- Mathematics - Dynamical Systems
- E-Print:
- 19 pages, 15 figures