中科院数学与系统科学研究院

动力系统研究中心

学术报告

报告人：Professor Raphael Krikorian (Ecole Polytechnique in France)

题  目：On local integrability of real analytic conservative diffeomorphisms

时  间：2024.04.06（星期六）10:30-11:30

地  点：南楼N933

摘  要： Let $A$ be the set of   real analytic diffeomorphism of the plane which admit the origin as an elliptic fixed point. We say that an element $f$ of $A$ is locally integrable at the origin if one can find a (possibly small) neighborhood of the origin on which $f$ is conjugated to a generalized rotation; we denote their set by $A_int$. Let  $A_symp$ be  the set of elements of $A$ that are symplectic  and $A_IP$ the set of elements of $A$ that have the intersection property.    I shall discuss the proofs of the following results: the sets $A_int\cap A_symp$ and $A_int\cap A_IP$ are dense for the real analytic topology in respectively $A_symp$ and $A_IP$.

报告人简介： Raphael Krikorian, is professor of the Ecole Polytechnique in France. He was a Member  of the University  Institute of France. He is a leading expert on Hamiltonian dynamical systems and spectral theory of quasiperiodic Schrodinger operator. For example, collaborating with A. Avila, he established the  global dichotomy of quasi-periodic cocycles, solved the zero-measure spectrum problem for the critical almost Mathieu operator;  he proved the generic divergence of the Birkhoff normal form of a real analytic symplectic diffeomorphism on a two-dimensional disk. His papers have been published in renowned journals such as Annals of Mathematics, Inventiones Mathematicae, Publ. Math. IHES, and he was an invited speaker at the 2018 International Congress of Mathematicians.