15 citations · 27 across the 4 of their papers we have counts for
4 papers
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…
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…
Semi-hyperbolic fibered rational maps and rational semigroups
Hiroki Sumi
We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assump…
Dimensions of Julia sets of expanding rational semigroups
Hiroki Sumi
We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in er…