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Subharmonic branching at a reversible 1:1 resonance

Maria-Cristina Ciocci (2005) JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. 11(13). p.1119-1135
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].
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
reversible systems, subharmonic branching, reversible maps, 1:1 resonance, SYSTEMS, BIFURCATIONS, SYMMETRY
journal title
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
J. Differ. Equ. Appl.
volume
11
issue
13
pages
1119 - 1135
Web of Science type
Article
Web of Science id
000233870100002
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.615 (2005)
JCR rank
75/151 (2005)
JCR quartile
2 (2005)
ISSN
1023-6198
DOI
10.1080/10236190500331214
language
English
UGent publication?
no
classification
A1
id
1200772
handle
http://hdl.handle.net/1854/LU-1200772
date created
2011-03-31 15:40:29
date last changed
2016-12-19 15:37:59
@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},
}

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.