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Iterates of maps with symmetryFixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Document ID
19890029451
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Chossat, Pascal
(Nice, Universite France)
Golubitsky, Martin
(Houston, University TX, United States)
Date Acquired
August 14, 2013
Publication Date
November 1, 1988
Publication Information
Publication: SIAM Journal on Mathematical Analysis
Volume: 19
ISSN: 0036-1410
Subject Category
Numerical Analysis
Accession Number
89A16822
Funding Number(s)
CONTRACT_GRANT: NAG2-279
CONTRACT_GRANT: NSF DMS-84-02604
Distribution Limits
Public
Copyright
Other

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