Subharmonic branching at a reversible 1:1 resonance

Autor:	Maria-Cristina Ciocci
Rok vydání:	2005
Předmět:	Algebra and Number Theory Unit circle Singularity theory Linearization Applied Mathematics Mathematical analysis Saddle-node bifurcation Codimension Fixed point Analysis Bifurcation Eigenvalues and eigenvectors Mathematics
Zdroj:	Journal of Difference Equations and Applications. 11:1119-1135
ISSN:	1563-5120 1023-6198
DOI:	10.1080/10236190500331214
Popis:	We investigate the bifurcation of q-periodic points from a fixed point of a 2-parameter family of n-dimensional reversible diffeomorphisms (n ≥ 4). The focus is on the codimension 2 non-semisimple 1:1 resonance case, that is, when the linearization at the fixed point has a pair of double eigenvalues on the unit circle, exp ( ± 2iπp/q) (with gcd(p, q) = 1), with geometric multiplicity 1. Through a modified version of Lyapunov Schmidt reduction, the reduced bifurcation equations are obtained. These are then analysed using reversible normal form theory and (reversible) singularity theory. We obtain the existence of two branches of symmetric q-periodic orbits bifurcating from the fixed point. We also describe the corresponding bifurcation scenario for a family of reversible systems in the case of a two-fold resonance, cfr. [12 5]. †A q-periodic orbit consits of q-points that are mapped into each other by Φλ
Databáze:	OpenAIRE
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