UNSPECIFIED (1998) k-symmetry and return maps of spacetime symmetric flows. NONLINEARITY, 11 (3). pp. 601-629. ISSN 0951-7715

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Abstract

A diffeomorphism U : Omega --> Omega is called a (reversing) k-symmetry of a dynamical system in Omega represented by the diffeomorphism f : Omega --> Omega if k is the smallest positive integer for which U is a (reversing) symmetry of f(k) (the k-times iterate of f), i.e. U o f(k) = f(+/-k) o U. In this paper we show how k-symmetry naturally arises in the context of return maps of flows with spacetime symmetries. We discuss the connection between periodic orbits of k-symmetric maps and symmetric periodic orbits of the flows they represent, and illustrate the application of our results in local bifurcation theory. We also provide a geometric interpretation of formal (Birkhoff) normal form symmetries fcr diffeomorphisms as a time-shift symmetry of a locally constructed spacetime symmetric suspension flow. Finally, we explain the occurrence of dual (representations of) reversing k-symmetry groups in k-symmetric maps in relation to different choices for the position of the surface of section for return maps of spacetime symmetric flows.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Date:	May 1998
Volume:	11
Number:	3
Number of Pages:	29
Page Range:	pp. 601-629
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/15724

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