You will need to choose a topic. It is usually related in some way to the main course (Dynamical systems) but it doesnâ€™t have to be. Some students write biographies about people associated with the subject , some write about applications of Dynamical systems to a particular problem in mathematics, physics, economics or some other field, some write on mathematical aspects that werenâ€™t covered in class.
I perfer to write biographies about people associated with the subject and I only need a outline with references and citations this time. If it goes well, we can work on the whole essay later on.