Multipliers of periodic orbits in spaces of rational maps
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- 11 March 2010
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 31 (1) , 197-243
Abstract
Given a polynomial or a rational function f we include it in 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 ρ⁄=1 as a function of the local coordinates, and establish a simple connection between the dynamical plane of f and the function ρ 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.Keywords
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