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Details van artikel 22 van 51 gevonden artikelen
| Titel: |
Generalized Lyapunov-Schmidt Reduction Method and Normal Forms for the Study of Bifurcations of Periodic Points in Families of Reversible Diffeomorphisms |
| Auteur: |
Ciocci, Maria-Cristina |
| Verschenen in: |
Journal of difference equations and applications |
| Paginering: | Jaargang 10 (2004) nr. 7 pagina's 621-649 |
| Jaar: |
2004-06 |
| Inhoud: |
We introduce a general reduction method for the study of periodic points near a fixed point in a family of reversible diffeomorphisms. We impose no restrictions on the linearization at the fixed point except invertibility, allowing higher multiplicities. It is shown that the problem reduces to a similar problem for a reduced family of diffeomorphisms, which is itself reversible, but also has an additional q-symmetry. The reversibility in combination with the q-symmetry translates to a q-symmetry for the problem, which allows to write down the bifurcation equations. Moreover, the reduced family can be calculated up to any order by a normal form reduction on the original system. The method of proof combines normal forms with the Lyapunov-Schmidt method, and makes repetitive use of the Implicit Function Theorem. As an application we analyze the branching of periodic points near a fixed point in a family of reversible mappings, when for a critical value of the parameters the linearization at the fixed point has either a pair of simple purely imaginary eigenvalues that are roots of unity or a pair of non-semisimple purely imaginary eigenvalues that are roots of unity with algebraic multiplicity 2 and geometric multiplicity 1. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 22 van 51 gevonden artikelen
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