Dynamical Systems Seminar: Hasina Akter (UNT): Real Analyticity of Hausdorff Dimension of Julia Sets of Parabolic Polynomials $f_{\lambda}(z)=z(1-z-\lambda z^2 )$, GAB 461 | Department of Mathematics

Dynamical Systems Seminar: Hasina Akter (UNT): Real Analyticity of Hausdorff Dimension of Julia Sets of Parabolic Polynomials $f_{\lambda}(z)=z(1-z-\lambda z^2 )$, GAB 461

Event Information
Event Location: 
GAB 461
Event Date: 
Repeats every week until Thu May 03 2012.
Thursday, April 12, 2012 - 3:00pm
Thursday, April 19, 2012 - 3:00pm
Thursday, April 26, 2012 - 3:00pm
Thursday, May 3, 2012 - 3:00pm

Abstract: Let $D_0$ denote the set of all parameters $\lambda\in\C\setminus\{0\}$ for which the cubic polynomial $f_\lambda$ is parabolic and has no parabolic or finite attracting periodic cycles other than $0$. We prove that $D_0$ contains a deleted neighborhood of the origin $0$. Our main result is that the function $D_0\ni\lambda\mapsto\text{HD}(J(f_\lambda))\in\R$ is real-analytic. This function ascribes to the polynomial $f_\lambda$ the Hausdorff dimension of its Julia set $J(f_\lambda)$. The theory of parabolic and hyperbolic graph directed Markov systems with infinite number of edges is used in the proofs.

Thinking about UNT?

It's easy to apply online. Join us and discover why we're the choice of over 37,000 students.

Apply now