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

@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},
     pages = {213--236},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {40},
     number = {1},
     year = {1990},
     doi = {10.5802/aif.1211},
     zbl = {0681.58022},
     mrnumber = {91e:58086},
     language = {en},
     url = {aif.centre-mersenne.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, Tome 40 (1990) no. 1, pp. 213-236. doi : 10.5802/aif.1211. https://aif.centre-mersenne.org/item/AIF_1990__40_1_213_0/

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