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Subharmonic branching at a reversible 1:1 resonance

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Abstract
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 resonancecase, that is, when the linearization at the fixed point has a pair of double eigenvalues on the unit circle, exp (+/- 2i pi p/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].
Keywords
reversible systems, subharmonic branching, reversible maps, 1:1 resonance, SYSTEMS, BIFURCATIONS, SYMMETRY

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Chicago
Ciocci, Maria-Cristina. 2005. “Subharmonic Branching at a Reversible 1:1 Resonance.” Journal of Difference Equations and Applications 11 (13): 1119–1135.
APA
Ciocci, M.-C. (2005). Subharmonic branching at a reversible 1:1 resonance. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 11(13), 1119–1135.
Vancouver
1.
Ciocci M-C. Subharmonic branching at a reversible 1:1 resonance. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. 2005;11(13):1119–35.
MLA
Ciocci, Maria-Cristina. “Subharmonic Branching at a Reversible 1:1 Resonance.” JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 11.13 (2005): 1119–1135. Print.
@article{1200772,
  abstract     = {We investigate the bifurcation of q-periodic points from a fixed point of a 2-parameter family of n-dimensional reversible diffeomorphisms (n {\textrangle}= 4). The focus is on the codimension 2 non-semisimple 1:1 resonancecase, that is, when the linearization at the fixed point has a pair of double eigenvalues on the unit circle, exp (+/- 2i pi p/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].},
  author       = {Ciocci, Maria-Cristina},
  issn         = {1023-6198},
  journal      = {JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS},
  keyword      = {reversible systems,subharmonic branching,reversible maps,1:1 resonance,SYSTEMS,BIFURCATIONS,SYMMETRY},
  language     = {eng},
  number       = {13},
  pages        = {1119--1135},
  title        = {Subharmonic branching at a reversible 1:1 resonance},
  url          = {http://dx.doi.org/10.1080/10236190500331214},
  volume       = {11},
  year         = {2005},
}

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