Friday September 06, 2019 2:30 PM  3:30 PM Math Tower P131
 Yusheng Luo, Stony Brook University
Classification of hyperbolic component with bounded escapeA hyperbolic component is said to have bounded escape if there is a sequence of rational maps which is degenerating as conjugacy classes, but for any period $p$, the multipliers of periodic points of period $p$ remain bounded. A hyperbolic component is said to have nested Julia sets if the Julia set is disconnected and there are two points that are separated by any Julia component.
In this talk we will show that a hyperbolic component has bounded escape if and only if it has nested Julia sets.

Friday September 13, 2019 2:30 PM  3:30 PM Math Tower P131
 Jonguk Yang, Stony Brook University
Structural Stability in the SemiSiegel Hénon FamilyConsider the family of strongly dissipative quadratic Hénon maps with a semiSiegel fixed point of goldenmean rotation number. Using a renormalization approach inspired by the work of Lyubich and Martens for Feigenbaum Hénon maps, we show that this family is structurally unstable. Combining this result with the work of Dujardin and Lyubich, we are able to conclude that the subset of semiSiegel Hénon maps that 1) have infinitely many sinks, or 2) have a disconnected Julia set, each form a dense subset within the family.
This is joint work with M. Yampolsky

Friday September 20, 2019 2:30 PM  3:30 PM Math Tower P131
 Alena Erchenko, Stony Brook University
Flexibility of Lyapunov exponents with respect to two classes of measures on the torusWe consider a family of Anosov areapreserving diffeomorphisms on the twotorus that are homotopic to a fixed Anosov automorphism. There are several interesting classes of invariant measures. We will concentrate on the invariant measure that is absolutely continuous with respect to the Lebesgue measure and the measure of maximal entropy. We show that positive Lyapunov exponents with respect to these two probability measures in the considered family of diffeomorphisms take on all values that satisfy some wellknown inequalities.

Friday September 27, 2019 2:30 PM  3:30 PM Math Tower P131
 Alex Kapiamba, University of Michigan
The Yoccoz inequality and parabolic implosionThe Yoccoz inequality provides a bound on the size of the limbs of the Mandelbrot set, however this bound is not sharp in most cases. Near parabolic parameters, for example the cusp of the main cardioid, the bound coming from the Yoccoz inequality appears to be far from optimal.
Parabolic implosion, the theory of perturbations of parabolic functions, provides tools to understand the geometry of the Mandelbrot set near parabolic parameters. In this talk I will discuss the possibility of using parabolic implosion to improve the Yoccoz inequality near parabolic parameters.

Friday October 04, 2019 2:30 PM  3:30 PM Math Tower P131
 Jeffrey Diller, University of Notre Dame
TBATBA

Friday October 11, 2019 2:30 PM  3:30 PM Math Tower P131
 Tanya Firsova, Kansas State University
TBATBA

Friday October 25, 2019 2:30 PM  3:30 PM Math Tower P131
 Giulio Tiozzo, University of Toronto
TBA

Friday November 08, 2019 2:30 PM  3:30 PM Math Tower P131
 Martin Bridgeman, Boston College
TBATBA

Friday November 22, 2019 2:30 PM  3:30 PM Math Tower P131
 Arnaud Chéritat, Insititut de Mathématiques de Toulouse, Paul Sabatier University
TBATBA

