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Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity

  • * Corresponding author: Maria Saprykina

    * Corresponding author: Maria Saprykina

B. Fayad was supported in part by Knut and Alice Wallenberg foundation, grant KAW 2016.0403, and by the ANR-15-CE40-0001. M.Saprykina was supported in part by the Swedish Research Council, VR 2015-04012

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  • Any $ C^d $ conservative map $ f $ of the $ d $-dimensional unit ball $ {\mathbb B}^d $, $ d\geq 2 $, can be realized by renormalized iteration of a $ C^d $ perturbation of identity: there exists a conservative diffeomorphism of $ {\mathbb B}^d $, arbitrarily close to identity in the $ C^d $ topology, that has a periodic disc on which the return dynamics after a $ C^d $ change of coordinates is exactly $ f $.

    Mathematics Subject Classification: Primary: 37C15.


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