题目：Computation of Normal Form on Discrete Dynamical Systems

报告人：Joan Gimeno, Postdoctoral Fellow（Universitat de Barcelona）

地点：致远楼101室

时间：2025年11月13日 10:00 - 11:00

摘要: I will present a semi-analytical algorithm for computing normal forms in discrete dynamical systems, such as Poincaré maps. The method involves calculating high-order derivatives using jet transport, applying coordinate transformations using composition and reverse operations to simplify the local dynamics around key objects. The method retains resonance terms crucial for understanding the system's behavior.

The algorithm is general, requiring only regularity assumptions, and is robust under parameter variations. I will discuss its application to Hamiltonian systems, with a focus on elliptic fixed points of a time flow map. Using normal form computations, I will construct high-dimensional twist maps and introduce a frequency recovery technique for visualizing high-dimensional tori within the discrete map.

To illustrate the practical utility of the method, I will apply it to the spatial Restricted Three-Body Problem (R3BP), demonstrating how these techniques can be used to gain insight into complex orbital dynamics near L4. The talk will include detailed examples, computational aspects of the method, and a discussion of its broader applications.

All are welcome to attend