An obstruction method for the destruction of invariant curves
type: Item
instance of: scholarly article
title: An obstruction method for the destruction of invariant curves
zbMATH Open document ID: 0612.58039
DOI: 10.1016/0167-2789(87)90222-3
author: Arturo Olvera
author: Carles Simó
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: An important point in a conservative dynamical system which is a parameter-depending perturbation of an integrable system is the destruction of the invariant curves. For small perturbations many invariant curves subsist according to KAM theorem. An increase in the size of perturbations produces, eventually, the destruction of the curves. The stochastic zone is then very large. In this paper we present for the standard map a geometrical approach to obtain values of the parameter for which no invariant curves exist. This is due to the existence of heteroclinic points. As it has been observed using other methods, there are several scaling properties in the phenomena which are also discussed here.
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 3990459
zbMATH Keywords: conservative dynamical system
zbMATH Keywords: KAM theorem
zbMATH Keywords: heteroclinic points
zbMATH Keywords: scaling properties
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90222-3
OpenAlex ID: W2000280157
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description: scientific article; zbMATH DE number 3990459