报告题目: Divergence of geometric normalizations for an elliptic fixed point in the plane

报告人：David Sauzin, 法国CNRS-IMCCE, 巴黎天文台

摘要: Classically, for a local analytic diffeomorphism  of  with a non-resonant elliptic fixed point (eigenvalues  with  real irrational), one can find formal normalizations, i.e. formal conjugacies to a formal diffeomorphism invariant under the group of rotations. Less demanding is the notion of a "geometric normalization" that we introduce: this is a formal conjugacy to a formal diffeomorphism which maps any circle centered at 0 to a circle centered at 0. Geometric normalizations are not unique, but they correspond in a natural way to a unique formal invariant foliation (any leaf is mapped to a leaf by ). Suppose that  is super-Liouville. We then show that, generically, all geometric normalizations are divergent, so there is no analytic invariant foliation. 

报告人简介:Dr. Sauzin is a senior researcher in mathematics at CNRS in France. He has worked intensively in the areas of nonlinear dynamical systems, summability theory, Ecalle's resurgence theory (which deals primarily with the behavior of asymptotic series or transseries), and mould calculus (a powerful combinatorial technique). He contributed to the theory of Hamiltonian perturbations (exponentially small separatrix splitting, Nekhoroshev's exponential stability theorem and examples of Arnold diffusion and wandering domains in Gevrey near-integrable systems), averaging theory in Gevrey classes, and holomorphic dynamics in one or two dimensions, and more recently applications of Resurgence to mathematical physics (Deformation quantization, quantum modularity and TQFT). He has made very fundamental contributions to Summability theory and Resurgence theory and is member of M. Kontsevich's team within the ERC Synergy Grant "Recursive and Exact New Quantum Theory" project:renewquantum.eu

报告时间：2023年10月19日（周四）上午11：00-12：00

报告地点：教二楼701

联系人：魏巧玲