Invariant curves near Hamiltonian–Hopf bifurcations of four-dimensional symplectic maps

Content Provider	Scilit
Author	Jorba, Àngel Ollé, Merce
Copyright Year	2004
Description	Journal: Nonlinearity In this paper, we give a numerical description of an extended neighbourhood of a fixed point of a symplectic map undergoing an irrational transition from linear stability to complex instability, i.e. the so-called Hamiltonian–Hopf bifurcation. We have considered both the direct and inverse cases.This study is based on numerical computation of the Lyapunov families of invariant curves near the fixed point. We show how these families, jointly with their invariant manifolds and the invariant manifolds of the fixed point, organize the phase space around the bifurcation.
Related Links	http://iopscience.iop.org/article/10.1088/0951-7715/17/2/019/pdf
Ending Page	710
Page Count	20
Starting Page	691
ISSN	09517715
e-ISSN	13616544
DOI	10.1088/0951-7715/17/2/019
Journal	Nonlinearity
Issue Number	2
Volume Number	17
Language	English
Publisher	IOP Publishing
Publisher Date	2004-01-27
Access Restriction	Open
Subject Keyword	Journal: Nonlinearity Invariant Curves Symplectic Maps Dimensional Symplectic Four Dimensional Hopf Bifurcations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics