SRB measures for C $\infty$ surface diffeomorphisms
| Autor: | Burguet, David |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A $C^\infty$ surface diffeomorphism admits a SRB measure if and only if the set \left \{x, \limsup_n \frac{1}{ n} \log \|d_xf^n \|> 0\right\} has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for $C^r$ surface diffeomorphisms with $+\infty>r>1$. |
| Databáze: | arXiv |
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