Chaotic transport by a turnstile mechanism in 4D symplectic maps

Many systems in nature, e.g. atoms, molecules and planetary motion, can be described as Hamiltonian systems. In such systems, the transport between different regions of phase space determines some of their most important properties like the stability of the solar system and the rate of chemical reactions. While the transport in lower-dimensional systems with two degrees of freedom is well understood, much less is known for the higher-dimensional case. A central new feature in higher-dimensional systems are transport phenomena due to resonance channels. In this thesis, we clarify the complex geometry of resonance channels in phase space and identify a turnstile mechanism that dominates the transport out of such channels. To this end, we consider the coupled standard map for numerical investigations as it is a generic example for 4D symplectic maps. At first, we visualize resonance channels in phase space revealing their highly non-trivial geometry. Secondly, we study the transport away from such channels. This is governed by families of hyperbolic 1D-tori and their stable and unstable manifolds. We provide an approach to measure the volume of a turnstile in higher dimensions as well as the corresponding transport. From the very good agreement of the two measurements we conclude that these structures are a suitable generalization of the well-known 2D turnstile mechanism to higher dimensions.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Technische Universität Dresden

Year

2020

Author dc:creator

• Hübner, Franziska

Contributors dc:contributor

• Ketzmerick, R.
• Padberg-Gehle, K.

• dynamical systems
• Hamiltonian systems
• transport
• higher dimensions
• 4D maps
• dynamische Systeme
• Hamilton'sche systeme
• höherdimensional
• 4D Abbildungen