Hiroki Sumi
Bowen Parameter and Hausdorff Dimension for Expanding Rational Semigroups.
Fri, 11/20/2009 - 16:01 — SomNambulAuthors: Hiroki Sumi, Mariusz Urbanski
Subjects: Dynamical Systems
AbstractWe consider the dynamics of rational semigroups (semigroups of rational maps)
on the Riemann sphere. We estimate the Bowen parameters (zeros of the pressure
functions) and the Hausdorff dimensions of the Julia sets of expanding finitely
generated rational semigroups.Dynamics of postcritically bounded polynomial semigroups III: classification of semi-hyperbolic semigroups and random Julia sets which are Jordan curves but not quasicircles.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Hiroki Sumi
Subjects: Dynamical Systems
AbstractWe investigate the dynamics of polynomial semigroups (semigroups generated by
a family of polynomial maps on the Riemann sphere) and the random dynamics of
polynomials on the Riemann sphere. Combining the dynamics of semigroups and the
fiberwise (random) dynamics, we give a classification of polynomial semigroups
$G$ such that $G$ is generated by a compact family $\Gamma $, the planar
postcritical set of $G$ is bounded, and $G$ is (semi-) hyperbolic.Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Rich Stankewitz, Hiroki Sumi
Subjects: Dynamical Systems
AbstractWe discuss the dynamic and structural properties of polynomial semigroups, a
natural extension of iteration theory to random (walk) dynamics, where the
semigroup $G$ of complex polynomials (under the operation of composition of
functions) is such that there exists a bounded set in the plane which contains
any finite critical value of any map $g \in G$. In general, the Julia set of
such a semigroup $G$ may be disconnected, and each Fatou component of such $G$
is either simply connected or doubly connected (\cite{Su01,Su9}).- Read more
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