Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori
type: Item
instance of: scholarly article
title: Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori
zbMATH Open document ID: 0664.58032
DOI: 10.1016/S0167-2789(98)90020-3
published in: Physica D
publication date: 1988-01-01T00:00:00Z
review text: An approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in Hamiltonian systems of one and a half degrees of freedom, similar to that of Escande and Doveil. It is a free semi-group with two generators. This scheme is solved exactly for its orbits, stable manifolds, unstable manifolds and critical set. Various results are found, including a Cantor set of universal fractal diagrams, the robustness of noble tori, and a scaling law for areas near critical circles.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 4086595
zbMATH Keywords: renormalisation scheme
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: free semi-group
zbMATH Keywords: orbits
zbMATH Keywords: stable manifolds
zbMATH Keywords: unstable manifolds
zbMATH Keywords: universal fractal diagrams
author: Robert S. MacKay
MaRDI profile type: Publication
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full work available at URL: s0167-2789(98)90020-3
OpenAlex ID: W1974286907
description: scientific article; zbMATH DE number 4086595