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Generic bifurcation of Hamiltonian systems with symmetry

Golubitsky, Martin and Stewart, Ian and Marsden, Jerrold (1987) Generic bifurcation of Hamiltonian systems with symmetry. Physica D, 24 (1-3). pp. 391-405. ISSN 0167-2789. doi:10.1016/0167-2789(87)90087-X.

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We study generic bifurcations of equilibria in one-parameter Hamiltonian systems with symmetry group Γ on the generalized eigenvalues of the linearized system go through zero. Theorem 3.3 classifies expected actions of Γ on the generalized eigenspace of this zero eigenvalue. Generic one degree of freedom symmetric systems is section 4; remarks concerning systems with more degrees of freedom are given in section 5.

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Additional Information:© 1987 Elsevier Science Publishers B.V. Received 2 May 1986; revised 19 June 1986. Available online 9 August 2002. We are grateful to Jerry Marsden, Debbie Lewis and Tudor Ratiu for suggesting to us that a generic description of transition in Hamiltonian systems with symmetry would be worthwhile. More accurately, this paper presents the results of a community discussion. The research of M.G. was supported in part by the AMSP program of DARPA, NASA Grant NAG-2279 and by NSF Grant DMS-8402604. The research of I.N.S. was supported in part by a grant from the Science and Engineering Research Council. The research of J.E.M. was supported in part by DOE contract DE-AT03-8SER12097.
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Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Science and Engineering Research CouncilUNSPECIFIED
Department of Energy (DOE)DE-AT03-8SER12097
Issue or Number:1-3
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ID Code:20443
Deposited By: Ruth Sustaita
Deposited On:03 Nov 2010 15:19
Last Modified:08 Nov 2021 23:59

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