ELFT HÍRADÓ

[Janos Asboth <asboth.janos AT wigner.mta.hu>]

MEGHÍVÓ

Wigner SZFI Kvantumoptika és Kvantuminformatika Csoport szemináriuma
Junius 3., kedd, 13 óra, SZFI Tanácsterem

Kozma Robert, Stony Brook University

Title: Limiting Behavior of Julia Sets of Perturbed Quadratic Maps

Abstract:
Even the simplest nonlinear function z^2+c gives rise to chaotic dynamics
resulting in very intricate mathematical objects such as the Mandelbrot
set, and Julia sets. In this talk we first go over some basic properties of
the Mandelbrot set, and Julia sets. We then go on to describe novel results
on the behavior of Julia sets of certain families of rational maps arising
from z^2+c by adding a small perturbation term λ/z^2 and taking the limit
as λ → 0. We will see that for certain c values the resulting Julia sets
have some astonishing geometric and topological properties. Using symbolic
dynamics and Cantor necklaces, we prove that as λ → 0, the Julia for this
family set evolves into a space-filling fractal curve.

Szeretettel várjuk az érdeklődőket,
 Asbóth János