Multipliers of periodic orbits in spaces of rational maps

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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.

Original languageAmerican English
Pages (from-to)197-243
Number of pages47
JournalErgodic Theory and Dynamical Systems
Volume31
Issue number1
DOIs
StatePublished - Feb 2011

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics

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