Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability
Annales de l'Institut Fourier, Volume 40 (1990) no. 1, p. 213-236

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.

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.

@article{AIF_1990__40_1_213_0,
     author = {Bonckaert, Patrick},
     title = {Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {40},
     number = {1},
     year = {1990},
     pages = {213-236},
     doi = {10.5802/aif.1211},
     zbl = {0681.58022},
     mrnumber = {91e:58086},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1990__40_1_213_0}
}
Bonckaert, Patrick. Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability. Annales de l'Institut Fourier, Volume 40 (1990) no. 1, pp. 213-236. doi : 10.5802/aif.1211. http://www.numdam.org/item/AIF_1990__40_1_213_0/

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