No round wandering domains for -diffeomorphisms of tori
We prove that if $n\geq 2$ , then there is no $C^{1}$ -diffeomorphism $f$ of the $n$ -torus such that $f$ is semi-conjugate to a minimal translation and its wandering domains are geometric balls. This improves a recent result of Navas, who proved it assuming $C^{n+1}$ regularity of $f$ .
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2019-11, Vol.39 (11), p.3127-3135 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove that if
$n\geq 2$
, then there is no
$C^{1}$
-diffeomorphism
$f$
of the
$n$
-torus such that
$f$
is semi-conjugate to a minimal translation and its wandering domains are geometric balls. This improves a recent result of Navas, who proved it assuming
$C^{n+1}$
regularity of
$f$
. |
|---|---|
| ISSN: | 0143-3857 1469-4417 |
| DOI: | 10.1017/etds.2018.11 |