On separatrix splitting of some quadratic area-preserving maps of the plane
type: Item
instance of: scholarly article
title: On separatrix splitting of some quadratic area-preserving maps of the plane
zbMATH Open document ID: 0924.58065
author: V. L. Chernov
published in: Regular and Chaotic Dynamics
publication date: 1999-08-19T00:00:00Z
review text: The simplest nontrivial examples of conservative dynamical systems with a chaotic trajectory behaviour are area-preserving maps of the plane. In the present paper, stable and unstable invariant curves of the map \[ QM(u,v)=(v+u+u^2,v+u^2) \] passing across the origin are presented in the form of Laplace's integrals from the same function but along different contours. An asymptotic of their difference calculated splitting of the map \[ HM (X,Y)= \bigl(Y+X+\varepsilon X(1-X),Y+\varepsilon X(1-X)\bigr). \] An asymptotic formula is given for a homoclinic invariant as \(\varepsilon\to 0\).
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1281641
zbMATH Keywords: chaotic trajectory
zbMATH Keywords: area-preserving maps
zbMATH Keywords: unstable invariant curves
zbMATH Keywords: homoclinic invariant
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
DOI: 10.1070/RD1998V003N01ABEH000060
description: scientific article; zbMATH DE number 1281641