Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Bonckaert, Patrick

Annales de l'Institut Fourier, Tome 40 (1990) no. 1, pp. 213-236.

On donne des conditions suffisantes pour que deux difféomorphismes, qui sont égaux sur une même variété invariante $V$ et dont les dérivées dans la direction normale sont aussi égales, soit conjugués ; on obtient en plus que l’homéomorphisme conjuguant $h$ satisfait des inégalités supplémentaires. Ces inégalités, qui impliquent l’existence de la dérivée normale de $h$ le long de $V$, servent à étendre cette conjugaison dans des régions où il y a des modules de stabilité.

We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.

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