Introduction to dynamical systems II

Academic year 2021/2022
Lecturer Stefano Marmi

Integrative teaching

Exercises

Examination procedure

Oral exam

Prerequisites

Introduzione ai sistemi dinamici I

Syllabus

Continued fractions, Gauss map. Lagrange theorem. Diophantine numbers. Liouville theorem and algebraic numbers.

Gottshalk-Hedlund theorem. Time reparametrization of flows and cohomolgical equation. 

Introduction to holomorphic dynamics: Julia and Fatou sets.

Ring of formal series. Convergent power series. Local dynamics: stability and linearizability. Linearization of holomorphic germs. Cremer counterexamples. Koenigs-Poincaré theorem. Siegel-Brjuno theorem. 

 

Bibliographical references

Appunti distribuiti agli studenti. 

Beardon: Iteration of Rational Functions

Devaney: An Introduction To Chaotic Dynamical Systems