Normalization of bundle holomorphic contractions and applications to dynamics
By Franccois Berteloot, Christophe Dupont, Laura Molino. 2007
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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.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2064cb56e178cafc600cce9fa6d2664c42a28c6b
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Bifurcation Currents in Holomorphic Families of Rational Maps (2012, background): “7 for endomorphisms of P; this has been done in [8].”