Article Contents
Article Contents

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

• * 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

• 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.

 Citation:

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