Lamb, Jeroen S. W. (1999) k-symmetry and return maps of spacetime symmetric flows. Nonlinearity, 11 (3). pp. 601-629. doi:10.1088/0951-7715/11/3/011 ISSN 0951-7715.

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Abstract

A diffeomorphism U : Ω → Ω is called a (reversing) k-symmetry of a dynamical system in Ω represented by the diffeomorphism f : Ω → Ω if k is the smallest positive integer for which U is a (reversing) symmetry of fk (the k-times iterate of f), i.e. U ○ fk = f±k ○ 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 for 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:	R Medicine > R Medicine (General)
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Official Date:	1 May 1999
Dates:	Date Event 1 May 1999 Published
Volume:	11
Number:	3
Page Range:	pp. 601-629
DOI:	10.1088/0951-7715/11/3/011
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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