Research
Interests: My current research comprises the fields
of holomorphic dynamical systems of one and several
complex variables, conformal iterated function systems
and smooth dynamical systems. This research also overlaps
and has applications to fractal geometry, number theory
and potential theory.
The research in the field
of holomorphic dynamical systems of one complex
variable focuses mostly on the geometry and ergodic
theory of transcendental entire (including exponential)
and meromorphic (including elliptic) functions as well
as on the questions of structural stability.
My research in the field
of holomorphic dynamical systems of several complex
variables mostly concerns with the applications of the
inverse thermodynamic formalism to the dimension problems
of holomorphic endomorphisms satisfying Axiom A.
The theory of infinite
iterated function systems developed within last ten
years jointly with Dr. Mauldin is being currently applied
to the problems coming from holomorphic dynamics, smooth
dynamics and Diophanitne approximations. This theory
is still studied itself especially in the contexts of
families of such systems and graph directed Markov systems.
In the area of smooth dynamical
systems I am concentrated on geometry and dynamics of
Smalle's horseshoes exhibiting parabolic type phenomena.
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