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January  2013, 33(1): 359-363. doi: 10.3934/dcds.2013.33.359

Continuation and bifurcation of multi-symmetric solutions in reversible Hamiltonian systems

André Vanderbauwhede 1,

1. 

Department of Pure Mathematics, Ghent University, Krijgslaan 281, B-9000 Gent, Belgium

Received  August 2011 Revised  February 2012 Published  September 2012

In this paper we discuss some general results on families of symmetric and doubly-symmetric solutions in reversible Hamiltonian systems having several independent first integrals. We describe a set-up for such solutions which allows the application of classical continuation and bifurcation results.
Keywords: Continuation, reversible Hamiltonian systems, multi-symmetric solutions., bifurcation.
Mathematics Subject Classification: Primary: 37J45, 37G40; Secondary: 37J4.
Citation: André Vanderbauwhede. Continuation and bifurcation of multi-symmetric solutions in reversible Hamiltonian systems. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 359-363. doi: 10.3934/dcds.2013.33.359
References:
[1]

F. J. Muñoz-Almaraz, E. Freire, J. Galán, E. J. Doedel and A. Vanderbauwhede, Continuation of periodic orbits in conservative and Hamiltonian systems, Physica D, 181 (2003), 1-38. doi: 10.1016/S0167-2789(03)00097-6.  Google Scholar

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F. J. Muñoz-Almaraz , E. Freire, J. Galán, and A. Vanderbauwhede, Continuation of Gerver's supereight choreography, Monografias de la Real Academia de Ciencias de Zaragoza, 30 (2006), 95-105.  Google Scholar

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F. J. Muñoz-Almaraz, E. Freire, J. Galán and A. Vanderbauwhede, Continuation of normal doubly symmetric orbits in conservative reversible systems, Celestial Mechanics & Dynamical Astronomy, 97 (2007), 17-47.  Google Scholar

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, http://www.maia.ub.es/ malmaraz/investigacion/Jaca/jaca.xml., ().   Google Scholar

show all references

References:
[1]

F. J. Muñoz-Almaraz, E. Freire, J. Galán, E. J. Doedel and A. Vanderbauwhede, Continuation of periodic orbits in conservative and Hamiltonian systems, Physica D, 181 (2003), 1-38. doi: 10.1016/S0167-2789(03)00097-6.  Google Scholar

[2]

F. J. Muñoz-Almaraz , E. Freire, J. Galán, and A. Vanderbauwhede, Continuation of Gerver's supereight choreography, Monografias de la Real Academia de Ciencias de Zaragoza, 30 (2006), 95-105.  Google Scholar

[3]

F. J. Muñoz-Almaraz, E. Freire, J. Galán and A. Vanderbauwhede, Continuation of normal doubly symmetric orbits in conservative reversible systems, Celestial Mechanics & Dynamical Astronomy, 97 (2007), 17-47.  Google Scholar

[4]

, http://www.maia.ub.es/ malmaraz/investigacion/Jaca/jaca.xml., ().   Google Scholar

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