“$z \mapsto z^2$”
Martedì 4 Giugno 2024, ore 14:00 - Lei Zhao (Augsburg University)
Abstract
This simple complex analytic mapping in the title induces a well-known correspondence between the planar Hooke and Kepler problems, and regularizes the planar Kepler problems with additional regular perturbations. This mapping has several extensions, and has more and more applications in dynamical systems. In this talk I shall illustrate its significance by presenting some recent results concerning enumerations of generalized periodic orbits in a periodically-forced Kepler problem and the construction and geometry of several new types of integrable mechanical billiards.
The talk is based on several joint works with A. Boscaggin (Turin) – R. Ortega (Granada), with A. Takeuchi (Augsburg), and with D. Jaud (Holzkirchen).
