Mini Course / Dynamics Learning Seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
February 07, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Dyi-Shing Ou, Stony Brook University
Nonexistence of wandering domains for infinitely renormalizable : I Hénon maps

The plan of the lectures is to prove the theorem: A strongly dissipative infinitely renormalizable Hénon-like map with stationary combinatorics does not have a wandering domain.

I will focus on the case of the period-doubling combinatorics. After the proof, I will say a few words about extending the proof to other stationary combinatorics.

The plan of the first talk is to cover the topics:
1. unimodal renormalization,
2. Hénon renormalization,
3. dynamics of an infinite period-doubling renormalizable Hénon map.

We will begin to prove the theorem in the following talk.


Wednesday
February 14, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Dyi-Shing Ou, Stony Brook University
Nonexistence of wandering domains for infinitely renormalizable Henon maps: part II

In this talk, we will prove the nonexistence of wandering domains for a strongly dissipative infinitely (period-doubling) renormalizable Henon-like map. I will classify the domain into two regions: the good region and the bad region. In the good region, the classical results from unimodal maps can be applied to Henon-like maps. In particular, if a wandering domain exists, the horizontal size of the elements in a rescaled orbit of the wandering domain (called the closest approach) expands at a definite rate. However, in the bad region, the Henon-like map behaves differently from a unimodal map and the property break down. I will show that the bad behavior can occur at most finitely many times in the rescaled orbit to conclude the theorem.

After proving the theorem, I will give some remarks on my recent work of extending the proof to other stationary combinatorics.


Wednesday
February 21, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Babak Modami, Stony Brook University
Minimal nonuniquely ergodic foliations on surfaces: I

Measured foliations (laminations) on surfaces are well-known examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichmüller and Weil-Petersson geodesics in the Teichmüller space.

In this mini-course, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations.
This work was inspired by a construction of Gabai and the earlier work of Lenzhen-Leininger-Rafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichmüller space (which won't be discussed in the minicourse).


Wednesday
February 28, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Babak Modami, Stony Brook University
Minimal nonuniquely ergodic foliations on surfaces: II

Measured foliations (laminations) on surfaces are well-known examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichmüller and Weil-Petersson geodesics in the Teichmüller space.

In this mini-course, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations. This work was inspired by a construction of Gabai and the earlier work of Lenzhen-Leininger-Rafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichmüller space (which won't be discussed in the minicourse).


Wednesday
March 14, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Rostislav Grigorchuk, Texas A&M University
TBA

TBA


Wednesday
March 28, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Sabya Mukherjee, Stony Brook University
TBA

TBA


Wednesday
April 04, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Sabya Mukherjee, Stony Brook University
TBA

TBA


Wednesday
April 18, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Dror Varolin, Stony Brook University
TBA

TBA


Wednesday
April 25, 2018

2:30 PM - 3:30 PM
Math Tower P-131
Dror Varolin, Stony Brook University
TBA

TBA


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