论文标题
4D符号图中混沌运输的部分障碍
Partial barriers to chaotic transport in 4D symplectic maps
论文作者
论文摘要
由于存在部分屏障，在哈密顿系统中的混沌运输通常受到限制，从而导致相位相位不同区域之间的通量有限。通常，2D符号图中最限制的部分屏障是基于cantorus，即破碎的1D圆环的cantor设置残余物。对于4D符号图，我们根据我们所谓的Cantorus-nhim建立了部分屏障，该壁层是一种正常双曲线不变的歧管（NHIM），其结构是cantorus的结构。使用通量公式，我们通过使用高阶的周期性NHIM近似于基于cantorus-nhim来确定基于cantorus-nhim的局部屏障的全局4D通量。此外，我们根据沿着共振通道的位置引入局部3D通量，该位置在存在缓慢的Arnold扩散的情况下与之相关。此外，对于由NHIM稳定和不稳定的歧管组成的部分屏障，我们利用定期NHIM来量化相应的通量。
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.
