55 citations · 174 across the 35 of their papers we have counts for
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Some counterexamples in dynamics of rational semigroups
Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi
We give an example of two rational functions with non-equal Julia sets that generate a rational semigroup whose completely invariant Julia set is a closed line segment. We also giv…
Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups
Rich Stankewitz, Hiroki Sumi
We discuss the dynamic and structural properties of polynomial semigroups, a natural extension of iteration theory to random (walk) dynamics, where the semigroup of complex pol…
Real analyticity of Hausdorff dimension for expanding rational semigroups
Hiroki Sumi, Mariusz Urbanski
We consider the dynamics of expanding semigroups generated by finitely many rational maps on the Riemann sphere. We show that for an analytic family of such semigroups, the Bowen p…
The equilibrium states for semigroups of rational maps
Hiroki Sumi, Mariusz Urbanski
We consider the dynamics of skew product maps associated with finitely generated semigroups of rational maps on the Riemann sphere. We show that under some conditions on the dynami…
Dynamics of postcritically bounded polynomial semigroups
Hiroki Sumi
We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, w…