Dynamical Systems and Applications: Geometrical, Topological, and Numerical Aspects

The school aims to introduce graduate students and young researchers to the modern theory of dynamical systems and its applications, with a focus on geometric, topological, and numerical methods. The courses will be focused on some key topics in low and high dimensional dynamics, including Hamiltonian systems, Celestial Mechanics, statistical properties of dynamical sysyems and their relation with the underlying geometric structures. The participants will be provided with an introduction to the basic material with the necessary background, before proceeding with the more advanced topics. Geometric and topological methods in dynamics provide a global picture of the structures that organize the dynamics. Thay are also essential in designing and implementing rigorous numerical experiments. The courses will survey a range of applications including classical mechanics, space mission design, dynamical astronomy, material science and biology. Besides lectures, they will also have sessions devoted to solving exercices and to computer experiments.