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

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

 
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Award ID(s):
2101464
PAR ID:
10351433
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Discrete & Continuous Dynamical Systems
Volume:
42
Issue:
2
ISSN:
1078-0947
Page Range / eLocation ID:
597
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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