Centralizer classification and rigidity for some partially hyperbolic toral automorphisms
| Autor: | Sandfeldt, Sven |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3934/jmd.2024013 |
| Popis: | In this paper we consider local centralizer classification and rigidity of some toral automorphisms. In low dimensions we classify up to finite index possible centralizers for volume preserving diffeomorphisms $f$ $C^{1}-$close to an ergodic irreducible toral automorphism $L$. Moreover, we show a rigidity result in the case that the centralizer of $f$ is large: If the smooth centralizer $Z^{\infty}(f)$ is virtually isomorphic to that of $L$ then $f$ is $C^{\infty}-$conjugate to $L$. In higher dimensions we show a similar rigidity result for certain irreducible toral automorphisms. We also classify up to finite index all possible centralizers for symplectic diffeomorphisms $C^{5}-$close to a class of irreducible symplectic automorphisms on tori of any dimension. Comment: 46 pages. Fixed an error in the proof of Claim 6.1 |
| Databáze: | arXiv |
| Externí odkaz: |
|