Studies of some trajectories in dynamical systems
This work is the bachelor semester project I did in the chair of Arithmetic Geometry (EPFL) in 2020, supervised by Alejandro Rivera. In this work, we investigate some problems of dynamical systems. The first part concerns my work on the still unsolved Katok's conjecture, a work that I begun in 2016 and continued here. The objective is to study periodic trajectories in triangles, I give insights on possible further investigations. The second part studies periodic trajectories in rational polygons and shows they are dense in the phase space of all the existing trajectories. The third part studies non-periodic trajectories and introduces KMS theorem (1986), a central theorem in ergodic theory. (Project is only available in French, do not hesitate to contact me if you want more information)
You can check out the full paper here.