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A study of resonance tongues near a Chenciner bifurcation using MatContM

Govaerts, Willy UGent, Kuznetsov, Yuri A, Meijer, Hil GE and Neirynck, Niels UGent (2011) Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011).
abstract
MatcontM is a matlab toolbox for numerical analysis of bifurcations of periodic orbits of maps. It computes codim 1 bifurcation curves and supports the computation of normal coefficients including branch switching from codim 2 points to secondary curves. Recently, the initialization and computation of connecting orbits was improved. Moreover, a graphical user interface was added enabling interactive control of all these computations. We demonstrate the use of the toolbox in a study of Arnol’d tongues near a degenerate Neimark-Sacker (Chenciner) bifurcation. Here we illustrate the recent theory of [4] how resonance tongues interact with a quasi-periodic saddle-node bifurcation of invariant curves in maps. Using normal form coefficients we find evidence for one of their cases, but not the other. Actually, we find another unfolding, i.e. a third possibility. We also give numerical evidence for the existence of a quasi-periodic cusp bifurcation of invariant curves.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
bifurcation, Map, Matcon, resonance
in
Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)
editor
Bernardini, D, Rega, G and Romeo, F
article number
MS-03
pages
5 pages
publisher
Sapienza Universita di Roma
place of publication
Rome, Italy
conference name
7th European Nonlinear Dynamics Conference (ENOC 2011)
conference location
Rome, Italy
conference start
2011-07-24
conference end
2011-07-29
ISBN
9788890623424
DOI
10.3267/ENOC2011Rome
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2129428
handle
http://hdl.handle.net/1854/LU-2129428
alternative location
http://w3.uniroma1.it/dsg/enoc2011/proceedings/pdf/Govaerts_et_al_6page.pdf
date created
2012-06-01 16:00:30
date last changed
2017-01-02 09:53:16
@inproceedings{2129428,
  abstract     = {MatcontM is a matlab toolbox for numerical analysis of bifurcations of periodic orbits of maps. It computes codim 1 bifurcation curves and supports the computation of normal coefficients including branch switching from codim 2 points to secondary curves. Recently, the initialization and computation of connecting orbits was improved. Moreover, a graphical user interface was added enabling interactive control of all these computations. We demonstrate the use of the toolbox in a study of Arnol{\textquoteright}d tongues near a degenerate Neimark-Sacker (Chenciner) bifurcation. Here we illustrate the recent theory of [4] how resonance tongues interact with a quasi-periodic saddle-node bifurcation of invariant curves in maps. Using normal form coefficients we find evidence for one of their cases, but not the other. Actually, we find another unfolding, i.e. a third possibility. We also give numerical evidence for the existence of a quasi-periodic cusp bifurcation of invariant curves.},
  articleno    = {MS-03},
  author       = {Govaerts, Willy and Kuznetsov, Yuri A and Meijer, Hil GE and Neirynck, Niels},
  booktitle    = {Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)},
  editor       = {Bernardini, D and Rega, G and Romeo, F},
  isbn         = {9788890623424},
  keyword      = {bifurcation,Map,Matcon,resonance},
  language     = {eng},
  location     = {Rome, Italy},
  pages        = {5},
  publisher    = {Sapienza Universita di Roma},
  title        = {A study of resonance tongues near a Chenciner bifurcation using MatContM},
  url          = {http://dx.doi.org/10.3267/ENOC2011Rome},
  year         = {2011},
}

Chicago
Govaerts, Willy, Yuri A Kuznetsov, Hil GE Meijer, and Niels Neirynck. 2011. “A Study of Resonance Tongues Near a Chenciner Bifurcation Using MatContM.” In Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011), ed. D Bernardini, G Rega, and F Romeo. Rome, Italy: Sapienza Universita di Roma.
APA
Govaerts, W., Kuznetsov, Y. A., Meijer, H. G., & Neirynck, N. (2011). A study of resonance tongues near a Chenciner bifurcation using MatContM. In D. Bernardini, G. Rega, & F. Romeo (Eds.), Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011). Presented at the 7th European Nonlinear Dynamics Conference (ENOC 2011), Rome, Italy: Sapienza Universita di Roma.
Vancouver
1.
Govaerts W, Kuznetsov YA, Meijer HG, Neirynck N. A study of resonance tongues near a Chenciner bifurcation using MatContM. In: Bernardini D, Rega G, Romeo F, editors. Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011). Rome, Italy: Sapienza Universita di Roma; 2011.
MLA
Govaerts, Willy, Yuri A Kuznetsov, Hil GE Meijer, et al. “A Study of Resonance Tongues Near a Chenciner Bifurcation Using MatContM.” Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011). Ed. D Bernardini, G Rega, & F Romeo. Rome, Italy: Sapienza Universita di Roma, 2011. Print.