Golubitsky, Martin and Marsden, Jerrold E. and Stewart, Ian and Dellnitz, Michael (1995) The constrained Liapunov-Schmidt procedure and periodic orbits. Fields Institute Communications, 4 . pp. 81-127. ISSN 1069-5265. http://resolver.caltech.edu/CaltechAUTHORS:20100810-121036542
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This paper develops the Liapunov-Schmidt procedure for systems with additional constraints such as having a first integral, being Hamiltonian, or being a gradient system. Similar developments for systems with symmetry, including reversibility, are well known, and the method of this paper augments and is consistent with that approach. One of the results states that the bifurcation equation for Hamiltonian systems is actually a Hamiltonian vector field. In general, we use "implicit constraints" to encode the information constraining the system. The method is applied to the Liapunov center theorem for reversible systems and systems with an integral, as well as to the Hamiltonian Hopf bifurcation and resonance bifurcations for Hamiltonian and reversible systems.
|Additional Information:||© 1995 American Matbematical Society. Research partially supported by NSF Grant DMS-9101836, the Texas Advanced Research Program (003652037) and The Fields Institute. Research partially supported by NSF Grant DM8-9302992 and The Fields Institute. Research partially supported by The Fields Institute. the Science and Engineering Research Council of the UK. and a European Community Laboratory Twinning grant (European Bifurcation Theory Group). Research partially supported by The Fields Institute. and a European Community Laboratory Twinning grant (European Bifurcation Theory Group). We would like to express our sincere thanks to Tom Bridges, Hans Duistermaat, Vivien Kirk, Victor LeBlanc, James Montaldi, Jan-Cees van der Meer, Tudor Ratiu, Jiirgen Scheurle, Alan Weinstein, and, in particular, Andre Vanderbauwhede, for useful comments and discussions.|
|Classification Code:||MSC: Primary 58F05; Secondary 58F14. 70K30|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||10 Aug 2010 21:55|
|Last Modified:||26 Dec 2012 12:18|
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