Multipliers of periodic orbits in spaces of rational maps

Details Multipliers of periodic orbits in spaces of rational maps Multipliers of periodic orbits in spaces of rational maps

2008-09-02

arxiv.org/abs/0809.0379v3

Mathematics

Dynamical Systems

Final version. To appear in ETDS

Scientific paper

Given a polynomial or a rational map f we associate to it a space of maps. We introduce local coordinates in this space, which are essentially the set of critical values of the map. Then we consider an arbitrary periodic orbit of f with multiplier \rho\not=1 as a function of the local coordinates, and establish a simple connection between the dynamical plane of f and the function \rho in the space associated to f. The proof is based on the theory of quasiconformal deformations of rational maps. As a corollary, we show that multipliers of non-repelling periodic orbits are also local coordinates in the space.

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