Jeroen S W Lamb 1996 Nonlinearity 9 537 doi:10.1088/0951-7715/9/2/015
Local bifurcations in k-symmetric dynamical systems
Jeroen S W Lamb
Show affiliationsRecommended by E Knobloch
A map 
is called a (reversing) k-symmetry of the dynamical system represented by the map 
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 
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.
- PACS
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05.45.-a Nonlinear dynamics and nonlinear dynamical systems
02.20.Qs General properties, structure, and representation of Lie groups
- MSC
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37C10 Vector fields, flows, ordinary differential equations
- Subjects
- Dates
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Issue 2 (March 1996)
Received 15 March 1995, in final form 28 November 1995
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Local bifurcations in k-symmetric dynamical systems
Jeroen S W Lamb 1996 Nonlinearity 9 537
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