Lamb, Jeroen S. W. (1999) Local bifurcations ink-symmetric dynamical systems. Nonlinearity, 9 (2). pp. 537-557. doi:10.1088/0951-7715/9/2/015 ISSN 0951-7715.

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Abstract

A map U : ℝd → ℝd is called a (reversing) k-symmetry of the dynamical system represented by the map L : ℝd → ℝd if k is the smallest positive integer for which U is a (reversing) symmetry of the kth iterate of L. We study generic local bifurcations of fixed points that are invariant under the action of a compact Lie group Σ that is a reversing k-symmetry group of the map L, on the basis of a normal form approach. We derive normal forms relating the local bifurcations of k-symmetric maps to local steady-state bifurcations of symmetric flows of vector fields. Alternatively, we also discuss the derivation of normal forms entirely within the framework of Taylor expansions of maps. We illustrate our results with some examples. © 1996 IOP Publishing Ltd and LMS Publishing Ltd.

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 January 1999
Dates:	Date Event 1 January 1999 Published
Volume:	9
Number:	2
Page Range:	pp. 537-557
DOI:	10.1088/0951-7715/9/2/015
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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