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Multipliers of periodic orbits in spaces of rational maps

Published online by Cambridge University Press:  11 March 2010

GENADI LEVIN
GENADI LEVIN*
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Israel (email: levin@math.huji.ac.il)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 1 , February 2011 , pp. 197 - 243
Copyright
Copyright © Cambridge University Press 2009

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