507 research outputs found
Normalization of bundle holomorphic contractions and applications to dynamics
We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic
contractions whose differentials d_0 G_n split regularly. The resonant
relations determining the normal forms hold on the moduli of the exponential
rates of contraction. Our results are actually stated in the framework of
bundle maps.
Such sequences of holomorphic contractions appear naturally as iterated
inverse branches of endomorphisms of CP(k). In this context, our normalization
result allows to precisely estimate the distortions of ellipsoids along typical
orbits. As an application, we show how the Lyapunov exponents of the
equilibrium measure are approximated in terms of the multipliers of the
repulsive cycles.Comment: 29 pages, references added, to appear in Ann. Inst. Fourie
On the geometry of bifurcation currents for quadratic rational maps
to appear in Ergodic Th. and Dyn. Syst.International audienceWe describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive (1, 1)-current on a two-dimensional complex projective space and then compute the Lelong numbers and the self-intersection of the extended current
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