A forgotten theorem on Z^k × R^m-action germs and related questions

(Preliminary version of the article appeared in Regular and Chaotic Dynamics 18, No. 6 (2013) dedicated to Alain Chenciner, 742-775)

Marc Chaperon (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

Two weakly hyperbolic smooth Z^k × R^m-action germs are smoothly conjugate if and only if they are formally conjugate, and such.

Keywords: AMS Subject Classification: 34A26; 34C20; 34C45; 34M35; 37C15; 37C85; 37D10; 37D15; 37D30; 37F75; 37G05; 01-02; 01A80 Hyperbolic; action germ; conjugacy; invariant manifold; normal form; flow; Lyapunov function; Cauchy problem; holomorphic vector field; first integral

Domains: Mathematics [math]; Dynamical Systems [math.DS]; Mathematics [math]; Differential Geometry [math.DG]

Marc Chaperon. A forgotten theorem on Z^k × R^m-action germs and related questions. 2022. ⟨hal-03850345⟩