Splitting of a small separatrix loop near the saddle-center bifurcation in area-preserving maps
type: Item
instance of: scholarly article
title: Splitting of a small separatrix loop near the saddle-center bifurcation in area-preserving maps
zbMATH Open document ID: 0942.37016
DOI: 10.1016/S0167-2789(99)00156-6
published in: Physica D
publication date: 2000-01-01T00:00:00Z
review text: The author deals with the splitting of a small separatrix loop that appears after the Bogdanov-Takens (saddle-center) bifurcation in an analytic family of area-preserving maps and proves that in general the splitting is described by almost the ``same formula'' as in the case of the standard map. More precisely, the author derives an asymptotic formula that describes the splitting, and studies the properties of the pre-exponential factor.
Mathematics Subject Classification ID: 37D30
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1394447
zbMATH Keywords: saddle-center bifurcation
zbMATH Keywords: separatrix splitting
zbMATH Keywords: area-preserving maps
zbMATH Keywords: asymptotic formula
zbMATH Keywords: pre-exponential factor
author: V. Gelfreich
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: s0167-2789(99)00156-6
OpenAlex ID: W2027757180
Wikidata QID: Q127774178
description: scientific article; zbMATH DE number 1394447