Extensions of quasiconformal deformations

1979 ◽  
pp. 321-328
Author(s):  
H. M. Reimann
Keyword(s):  
Quasiconformal Deformations

scholarly journals Multipliers of periodic orbits in spaces of rational maps

2010 ◽  
Vol 31 (1) ◽  
pp. 197-243 ◽  
Author(s):  
GENADI LEVIN
Keyword(s):  
Periodic Orbit ◽  
Rational Function ◽  
Periodic Orbits ◽  
Critical Values ◽  
Rational Maps ◽  
Dynamical Plane ◽  
Local Coordinates ◽  
Quasiconformal Deformations

AbstractGiven 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.

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