Converse KAM: theory and practice
type: Item
instance of: scholarly article
title: Converse KAM: theory and practice
zbMATH Open document ID: 0585.58032
DOI: 10.1007/BF01209326
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: Whereas KAM theory deals with the existence of invariant circles of area preserving maps, the present paper is concerned with ``converse KAM theorems'', i.e. criteria for nonexistence of invariant circles. There are several such theorems available in the literature, which are ''unified, extended, reinterpreted, and applied''. As an example a computer proof is given for the fact that the so-called ``standard map'' \(p'=p-(k/2\pi) \sin 2\pi x\), \(x'=x+p'\) has no rotational invariant circles for \(| k| \geq 63/64\). The paper is self-contained and provides a useful survey of converse KAM theory.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37-04
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 3938098
zbMATH Keywords: following orbits
zbMATH Keywords: standard map
zbMATH Keywords: orbits of minimum action
zbMATH Keywords: KAM theory
zbMATH Keywords: invariant circles of area preserving maps
zbMATH Keywords: converse KAM theory
author: Robert S. MacKay
author: Ian C. Percival
reviewed by: Volker Perlick
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01209326
OpenAlex ID: W2052105844
description: scientific article; zbMATH DE number 3938098