Dynamical Systems Seminar

from Tuesday
January 01, 2019 to Friday
May 31, 2019
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Friday
February 01, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Boris Solomyak, University of Bar-Ilan
On the dimension of Furstenberg measure for $SL(2,R)$ random matrix products and the Diophantine condition in matrix groups

Let $μ$ be a finitely supported measure on $SL(2,R)$ generating a non-compact and totally irreducible subgroup. Furstenberg proved that there is a unique stationary measure for the induced action on the projective line (now often called the ``Furstenberg measure''), with a positive Lyapunov exponent. In joint work with M. Hochman, we computed the Hausdorff dimension of the Furstenberg measure, assuming a Diophantine condition on the support of $μ$. I will also discuss some follow-up results on the Diophantine property in matrix groups and on the dimension of the support of the Furstenberg measure, joint with Y. Takahashi.


Friday
February 08, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Liviana Palmisano, Uppsala University
Newhouse Laminations

We prove that the Newhouse phenomenon has a codimension 2 nature. Namely, there exist codimension 2 laminations of maps with infinitely many sinks. The leaves of the laminations are smooth and the sinks move simultaneously along the leaves. These Newhouse laminations occur in unfoldings of rank-one homoclinic tangencies.
As consequence, in the space of polynomial maps, there are examples of:
-two dimensional Hénon maps with finitely many sinks and one strange attractor,
-Hénon maps, in any dimension, with infinitely many sinks,
-quadratic Hénon-like maps with infinitely many sinks and one period doubling attractor,
-quadratic Hénon-like maps with infinitely many sinks and one strange attractor,
-two dimensional Hénon maps with finitely many sinks and two period doubling attractors,
-quadratic Hénon-like maps with finitely many sinks, two period doubling attractors and one strange attractor.


Friday
February 22, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Kasra Rafi, University of Toronto
Counting of the number of simple closed curves on a surface, revisited

TBA


Friday
March 01, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Zoran Sunic, Hofstra University
Schreier spectra of some iterated monodromy groups

We discuss calculation of spectra of several iterated monodromy groups, such as the Hanoi Towers group $H$ and one of its subgroups, the “tangled odometers group“ $T$.

The Hanoi Towers group is the iterated monodromy group of the $3$-dimensional, post-critically finite, rational map $z→ z^2 – 16/(27z)$ and it models the well-known Hanoi Towers Problem. The subgroup $T$ is the iterated monodromy group of the post-critically finite, cubic polynomial $z→ -z^3/2 + 3z/2$ whose two critical points are fixed.

The groups act on the ternary rooted tree and on its boundary. The spectrum of the Schreier graphs of these actions were, in both cases, shown to consist of a countable set of isolated points and a Cantor set to which the isolated points accumulate via backward iterations of a quadratic polynomial. In both cases, the calculation is facilitated by first introducing a higher dimensional rational map, which is then shown to be semi-conjugate to a one-dimensional map.

Time permitting, we will also discuss the case of iterated monodromy groups of arbitrary conservative polynomials.


Friday
March 08, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Jonguk Yang, University of Michigan
TBA

TBA


Friday
April 05, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Malik Younsi, University of Hawaii
TBA

TBA


Friday
April 12, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Jing Tao, University of Oklahoma
TBA

TBA


Friday
April 19, 2019

2:30 PM - 3:30 PM
Math Tower P-131
Saeed Zakeri, CUNY
TBA

TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars