On the geometry of transport in phase space. I. Transport in k-degree-of- freedom Hamiltonian systems, \(2\leq k<\infty\)
type: Item
instance of: scholarly article
title: On the geometry of transport in phase space. I. Transport in k-degree-of- freedom Hamiltonian systems, \(2\leq k<\infty\)
zbMATH Open document ID: 0705.58018
DOI: 10.1016/0167-2789(90)90159-M
author: Stephen Wiggins
published in: Physica D
publication date: 1990-01-01T00:00:00Z
review text: The transport theory for 2-dimensional Hamiltonian systems is facilitated by the existence of (complete or partial) barriers (invariant tori, stable and unstable manifolds, cantorus) which permit to estimate the transport rate in the phase space. Using the perturbation argument, the author determines a large class of higher dimensional Hamiltonian systems with quite analogous property: there exist certain normally hyperbolic invariant subsets of codimension one in every level set of the Hamiltonian. Then the mechanism of the transport (in particular the lobe dynamics, the conservation rules, turnstiles) can be investigated in the same manner as in the case of two-degree of freedom. A thorough discussion of the Hamiltonian \[ H_{\epsilon}=v^ 2-\cos \phi +y^ 2_ 1+\omega^ 2_ 1x^ 2_ 1+y^ 2_ 2+\omega^ 2_ 2x^ 2_ 2+\epsilon \tilde H \] and several general remarks concerning the transport near resonances and the Arnold diffusion conclude the paper.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 82C70
zbMATH DE Number: 4157526
zbMATH Keywords: Poincaré map
zbMATH Keywords: turnstile
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: transport
zbMATH Keywords: lobe dynamics
zbMATH Keywords: conservation rules
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4157526