Institut für Theoretische Physik and Center for Dynamics, Technische Universität Dresden, 01062 Dresden, Germany.
Chaos. 2023 Jan;33(1):013125. doi: 10.1063/5.0130682.
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.
哈密顿系统中的混沌输运通常由于部分障碍的存在而受到限制，这导致了相空间中不同区域之间的通量有限。通常，二维辛映射中最具限制性的部分障碍是基于cantorus 的，即一维环面断裂的Cantor 集残余。对于四维辛映射，我们建立了一个基于我们所谓的 cantorus-NHIM（具有 cantorus 结构的正则双曲不变流形）的部分障碍。使用通量公式，我们通过用高阶周期 NHIM 来近似来确定基于 cantorus-NHIM 的全局 4D 通量。此外，我们引入了一个依赖于共振通道位置的局部 3D 通量，这在存在缓慢 Arnold 扩散时是相关的。此外，对于由 NHIM 的稳定和不稳定流形组成的部分障碍，我们利用周期 NHIM 来量化相应的通量。
