Bifurcation currents in holomorphic dynamics on ${\bf P}^k$
| dc.creator | Bassanelli, Giovanni | |
| dc.creator | Berteloot, François | |
| dc.date | 2005-07-27 | |
| dc.date | 2005-09-21 | |
| dc.date.accessioned | 2026-07-07T06:18:30Z | |
| dc.date.available | 2026-07-07T06:18:30Z | |
| dc.description | We establish a formula for the sum of the Lyapounov exponents of an holomorphic endomorphism of ${\bf P}^k$. For an holomorphic family of such endomorphisms we define the {\em bifurcation current} as $dd^cL$ and show that it vanishes when the repulsive cycles move holomorphically. We then prove a formula which relates this current with the interaction between the Green current and the current of integration on the critical set. In the 1-dimensional case (i.e. for ${\bf P}^1$) we find a geometrical description of the support of this current and its powers. Finally we introduce the {\em bifurcation measure} giving some applications. This last part may be interpreted as a generalization of Mane-Sad-Sullivan theory based on pluri-potentialist methods. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507555 | |
| dc.identifier | http://arxiv.org/abs/math/0507555 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94755 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | 37F45; 37F10 | |
| dc.title | Bifurcation currents in holomorphic dynamics on ${\bf P}^k$ | |
| dc.type | text |