Resonances and transport in the sawtooth map
type: Item
instance of: scholarly article
title: Resonances and transport in the sawtooth map
zbMATH Open document ID: 0722.58019
DOI: 10.1016/0167-2789(90)90037-P
author: Q. Chen
author: N. W. Murray
author: Itzhack Dana
author: J. D. Meiss
author: Ian C. Percival
published in: Physica D
publication date: 1990-01-01T00:00:00Z
review text: The paper obtains the very detailed investigation of the sawtooth map T of a cylinder on itself, which has a form \[ T(x,p)=(x+p+K(x-0.5),p+K(x- 0,5)),\quad (x,p)\in S^ 1\times {\mathbb{R}},\quad K\in {\mathbb{R}}^+. \] This map is considered as a model for chaotic Hamiltonian system. Analytical expressions are obtained for its cantori and resonances. The partial flux transferred from one resonance to another is determined by the degree of overlap of their turnstiles. The survival probability within a resonance is calculated using the Markov model. A construction of the horseshoe for trapped orbits is provided.
reviewed by: A. Klíč
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 4190755
zbMATH Keywords: sawtooth map
zbMATH Keywords: chaotic Hamiltonian system
zbMATH Keywords: cantori
zbMATH Keywords: partial flux
zbMATH Keywords: resonance
zbMATH Keywords: Markov model
zbMATH Keywords: horseshoe
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4190755