Divergent diagrams of folds and simultaneous conjugacy of involutions

Solange Mancini; Miriam Manoel; Marco Antonio Teixeira

doi:10.3934/dcds.2005.12.657

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2005, Volume 12, Issue 4: 657-674. Doi: 10.3934/dcds.2005.12.657

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Divergent diagrams of folds and simultaneous conjugacy of involutions

1.
Departamento de Matemática, IGCE, Universidade Estadual Paulista, 13500-230 Caixa Postal 178, Rio Claro, SP
2.
Departamento de Matemática, ICMC, Universidade de São Paulo, 13560-970 Caixa Postal 668, São Carlos, SP
3.
Departamento de Matemática, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-970, Campinas, S.P.

Received: November 2003

Revised: September 2004

Published: July 2005

Abstract / Introduction Related Papers Cited by

Abstract

In this work we show that the smooth classification of divergent diagrams of folds $(f_1, \ldots, f_s) : (\mathbb R^n,0) \to (\mathbb R^n \times \cdots \times \mathbb R^n,0)$ can be reduced to the classification of the $s$-tuples $(\varphi_1, \ldots, \varphi_s)$ of associated involutions. We apply the result to obtain normal forms when $s \leq n$ and $\{\varphi_1, \ldots, \varphi_s\}$ is a transversal set of linear involutions. A complete description is given when $s=2$ and $n\geq 2$. We also present a brief discussion on applications of our results to the study of discontinuous vector fields and discrete reversible dynamical systems.

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Mathematics Subject Classification: 34G10, 47D06, 58F11, 92D25.

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