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Une caractérisation des endomorphismes de Lattès par leur mesure de Green
| Content Provider | Semantic Scholar |
|---|---|
| Author | Berteloot, François Dupont, Christophe |
| Copyright Year | 2005 |
| Abstract | We show that the Lattes endomorphisms are the only holomorphic endomorphisms of the complex $k$-dimensional projective space whose measure of maximal entropy is absolutely continuous with respect to the Lebesgue measure. As a consequence, Lattes endomorphisms are also characterized by other extremal properties as the maximality of the Hausdorff dimension of their measure of maximal entropy or the minimality of their Liapounov exponents. Our proof uses a linearization method which is of independant interest and a previous characterization by the regularity of the Green current. |
| Starting Page | 433 |
| Ending Page | 454 |
| Page Count | 22 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/CMH/21 |
| Volume Number | 80 |
| Alternate Webpage(s) | https://hal.archives-ouvertes.fr/hal-00003748/document |
| Alternate Webpage(s) | http://www.ems-ph.org/journals/show_pdf.php?iss=2&issn=0010-2571&rank=9&vol=80 |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0501034v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.4171/CMH%2F21 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
