Partial barriers to chaotic transport in 4D symplectic maps
arXiv:2210.09863 · doi:10.1063/5.0130682
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 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.
arXiv comment19 pages, 15 figures
References in corpus (27)
- Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
- Thirty Years of Turnstiles and Transport
- The dynamical structure of the MEO region: long-term stability, chaos, and transport
- Detecting chaos in particle accelerators through the frequency map analysis method
- Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
- Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river
- The speed of Arnold diffusion
- Bifurcations of transition states: Morse bifurcations
- Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps
- Universal Quantum Localizing Transition of a Partial Barrier in a Chaotic Sea
- Sticky obstacles to intramolecular energy flow
- What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?
- Extracting Multidimensional Phase Space Topology from Periodic Orbits
- The chaotic set and the cross section for chaotic scattering beyond in 3 degrees of freedom
- Bifurcations of families of 1D-tori in 4D symplectic maps
- Binary contraction method for the construction of time-dependent dividing surfaces in driven chemical reactions
- 3D billiards: visualization of regular structures and trapping of chaotic trajectories
- Resonance Zones and Lobe Volumes for Volume-Preserving Maps
- Chaotic transport of navigation satellites
- Localization of Chaotic Resonance States due to a Partial Transport Barrier
- Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
- Drift and its mediation in terrestrial orbits
- Barriers to Transport and Mixing in Volume-Preserving Maps with Nonzero Flux
- Intramolecular vibrational energy redistribution from a high frequency mode in the presence of an internal rotor: Classical thick-layer diffusion and quantum localization
- Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
- Analytical Expression for Low-dimensional Resonance Island in 4-dimensional Symplectic Map
- Dynamics near Resonance Junctions in Hamiltonian Systems