Mathematical Study and Visualization of Complex Dynamical Systems

The aim of this project is to
visualize hardly accessable
phenomena within complex
dynamical systems, such as:
the parabolical implosion,
holomorfic surgery and
renormalization, as well as
to illustrate the elementary
phenomena: iteration,
topological models and
potential theoretical tools.
In order to be able to
visualize the phenomena
mentioned, thorough
mathematical studies are
necessary. A number of known
proofs need to be modified
and new proofs established in
order to achieve the
mathematical visualization.
The visualization media is
the video, but it is accompanied
with explicatory material,
interactive programs
(possibly as CD-ROM) and
finally classical
mathematical publications.
The receiving audience
includes mathematical
high-school students to
fellow researchers within the
area. Keywords: Holomorphic
dynamics, algorithms,
computer animation.