Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
COMD Research Seminar Series: Renormalization Of Unimodal Real Hénon Maps
To participate in this seminar, please register HERE.
In the mid 1970s, Feigenbaum and Coullet-Tresser independently observed that the period-doubling cascade in the family of real quadratic polynomials exhibit a universal scaling property. They introduced renormalization as a conjectural explanation of this phenomenon. Since then, this idea has been developed into a deep and rigorous theory, and as a result, we now have a complete understanding of the dynamics of any unimodal map on an interval.
In dimension two, real Hénon maps provide the simplest non-trivial analogs of real quadratic polynomials. However, despite being one of the best studied class of examples in the field, the dynamical structures of these maps still remains a wide open area of research.
In this talk, I will present a generalization of the renormalization theory of one-dimensional unimodal maps that applies to real Hénon maps. The main result will be a priori bounds for substantially dissipative, infinitely renormalizable Hénon maps that have a unique "critical point" (the meaning of which will be explained during the talk). This is based on an ongoing joint project with Sylvain Crovisier, Mikhail Lyubich and Enrique Pujals
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