On decomposable rational maps

On Bicritical Rational Maps

This is a preliminary investigation of the geometry and dynamics of rational maps with only two critical points.

The discrete dynamics of monotonically decomposable maps.

We extend results of Gouzé and Hadeler (in Nonlinear World 1:23-34, 1994) concerning the dynamics generated by a map on an ordered metric space that can be decomposed into increasing and decreasing parts. Our main results provide sufficient conditions for the existence of a globally asymptotically stable fixed point for the map. Applications to discrete-time, stage-structured population models ...

On “thermodynamics” of Rational Maps Ii. Non-recurrent Maps

The pressure function p(t) of a non-recurrent map is real analytic on some interval (0, t∗) with t∗ strictly greater than the dimension of the Julia set. The proof is an adaptation of the well-known tower techniques to the complex dynamics situation. In general, p(t) need not be analytic on the whole positive axis.

The Space of Rational Maps on P1

The set of morphisms : P 1 ! P 1 of degree d is parametrized by an aane open subset Rat d of P 2d+1. We consider the action of SL 2 on Rat d induced by the conjugation action of SL 2 on rational maps; that is, f 2 SL 2 acts on via f = f ?1 f. The quotient space M d = Rat d =SL 2 arises very naturally in the study of discrete dynamical systems on P 1. We prove that M d exists as an aane integral...

The Information Metric on Rational Maps