k-symmetry and return maps of spacetime symmetric flows
UNSPECIFIED. (1998) k-symmetry and return maps of spacetime symmetric flows. NONLINEARITY, 11 (3). pp. 601-629. ISSN 0951-7715Full text not available from this repository.
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|
|Official Date:||May 1998|
|Number of Pages:||29|
|Page Range:||pp. 601-629|
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