Thirty Years of Turnstiles and Transport

Abstract

To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem over the past thirty years. Primary measures of transport for volume-preserving maps include the exiting and incoming fluxes to a region. For area-preserving maps, transport is impeded by curves formed from invariant manifolds that form partial barriers, e.g., stable and unstable manifolds bounding a resonance zone or cantori, the remnants of destroyed invariant tori. When the map is exact volume preserving, a Lagrangian differential form can be used to reduce the computation of fluxes to finding a difference between the action of certain key orbits, such as homoclinic orbits to a saddle or to a cantorus. Given a partition of phase space into regions bounded by partial barriers, a Markov tree model of transport explains key observations, such as the algebraic decay of exit and recurrence distributions.

Updated and corrected version

References in corpus (11)

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• Simulation of non-resonant stellarator divertor
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• Magnetic turnstiles in nonresonant stellarator divertor
• Exploration of Non-Resonant Divertor Features on the Compact Toroidal Hybrid
• Partial barriers to chaotic transport in 4D symplectic maps
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• Further results on the power-law decay of the fraction of the mixed eigenstates in kicked-top model with mixed-type classical phase space
• Nearly integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence
• Classical Drift in the Arnold Web Induces Quantum Delocalization Transition
• Designing robust trajectories by lobe dynamics in low-dimensional Hamiltonian systems
• Phase space structures causing the reaction rate decrease in the collinear hydrogen exchange reaction
• The Maintenance of Coherent Vortex Topology by Lagrangian Chaos in Drift-Rossby Wave Turbulence
• Topological Dynamics of Volume-Preserving Maps Without an Equatorial Heteroclinic Curve
• Diffusion and escape times in the open-leaky standard map
• Design of low-energy transfers in cislunar space using sequences of lobe dynamics
• Recurrence and Stickiness in the Noisy Harper Map