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arXiv · 2103.15530

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

Bassam Fayad·Maria Saprykina
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Abstract

Any $C^d$ conservative map $f$ of the $d$-dimensional unit ball $\mathbb B^d$ 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 $f$.

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Bassam Fayad, Maria Saprykina. 2021-03-29. Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity. https://arxiv.org/abs/2103.15530

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