Complex Analysis and Dynamics Seminar at CUNY's GC

Complex Analysis and Dynamics Seminar

Department of Mathematics

Graduate Center of CUNY

Fridays 2:00 - 3:00 pm

Room 5417

Organizers: Ara Basmajian, Patrick Hooper, Jun Hu, Saeed Zakeri

Past seminars:

Fall 2021:

Nov 19: Enrique Pujals (Graduate Center of CUNY)
Dynamics of Hénon Maps with Zero Entropy

I will focus on surface diffeomorphisms with zero entropy: Can the dynamics of these 'simple' systems be described? How does it bifurcate to positive entropy systems? These questions will be discussed for a class of volume-contracting surface diffeomorphisms whose dynamics is intermediate between one-dimensional dynamics and general surface dynamics. It includes the dynamics of any Hénon diffeomorphism with Jacobian smaller than 1/4.

For that type of systems, first we will try to prove that any Hénon map with zero entropy and Jacobian smaller than 1/4 "is renormalized" (this is part of joint work with S. Crovisier and C. Tresser).

Later, we will discuss work in progress with Sylvain Crovisier, Misha Lyubich and Jonguk Jang about the bounded geometry of those renormalizable systems.