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 language | American English |
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Pages (from-to) | 197-243 |
Number of pages | 47 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 31 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2011 |