Dynamique des applications polynomiales semi-regulieres
| dc.creator | Dinh, T. C. | |
| dc.creator | Sibony, N. | |
| dc.date | 2002-11-20 | |
| dc.date.accessioned | 2026-07-07T04:53:08Z | |
| dc.date.available | 2026-07-07T04:53:08Z | |
| dc.description | For any proper polynomial map $f:C^k\longrightarrow C^k$ define the function αas $$α(z):=\limsup_{n\to\infty} \frac{\log^+\log^+|f^n(z)|}{n} where \log^+:=\max(\log, 0).$$ Let f=(P_1,...,P_k) be a proper polynomial map. We define a notion of s-regularity using the extension of f to P^k. When f is (maximally) regular we show that the function αis l.s.c and takes only finitely many values: 0 and d_1, ..., d_k, where d_i:=deg P_i. We then describe dynamically the sets (α\leq d_i). If d_i>1, this allows us to construct the equilibrium measure μassociated to f as a generalized intersection of positive currents. We then gives an estimate of the Hausdorff dimension of μ. This is a special case of our results. We extend the approach to the larger class of (π,s)-regular maps. This gives an understanding of the biggest values of α. The results can be applied to construct dynamically interesting measures for automorphisms. | |
| dc.description | 29 pages, nouvelle version | |
| dc.identifier | https://arxiv.org/abs/math/0211324 | |
| dc.identifier | http://arxiv.org/abs/math/0211324 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65731 | |
| dc.subject | Dynamical Systems | |
| dc.title | Dynamique des applications polynomiales semi-regulieres | |
| dc.type | text |