Hyperbolic repellers for algebraic functions

Abstract

This paper deals with the iteration of algebraic functions, i.e. (in general) multivalued self maps of the Riemann sphere deened by z 7 ! w if P (z; w) = 0, where P is a polynomial in two complex variables. The notion of a hyperbolic repeller is introduced and illustrated by several examples. We prove that hyperbolic repellers are orbit stable under perturbations.

Cite this paper

@inproceedings{Ochs1997HyperbolicRF, title={Hyperbolic repellers for algebraic functions}, author={Gunter Ochs}, year={1997} }