Marc Chaperon, “A Forgotten Theorem on <nobr>$\mathbf{Z}^k \times \mathbf{R}^m$</nobr>-action Germs and Related Questions”, Regul. Chaotic Dyn., 2013, Volume 18, Issue 6,Pages <nobr>742

This article is cited in 5 papers

A Forgotten Theorem on $\mathbf{Z}^k \times \mathbf{R}^m$-action Germs and Related Questions

Marc Chaperon

Institut de Mathématiques de Jussieu, Université Paris 7, Bâtiment Sophie Germain, Case 7012, 75205 PARIS CEDEX 13, France

Abstract: Two weakly hyperbolic smooth $\mathbf{Z}^k \times \mathbf{R}^m$-action germs are smoothly conjugate if and only if they are formally conjugate, and such.

Keywords: Hyperbolic, action germ, conjugacy, invariant manifold, normal form, flow, Lyapunov function, Cauchy problem, holomorphic vector field, first integral.

MSC: 34A26, 34C20, 34C45, 34M35, 37C15, 37C85, 37D10, 37D15, 37D30, 37F75, 37G05, 01-02, 01A80

Received: 01.10.2013
Accepted: 22.11.2013

Language: English

DOI: 10.1134/S1560354713060130