Introduction to dynamical systems II
Period of duration of course
Introduzione ai sistemi dinamici I
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.
The goal of the course is to introduce the fundamental
notions of the modern theory of dynamical systems.
Appunti distribuiti agli studenti.
Beardon: Iteration of Rational Functions
Devaney: An Introduction To Chaotic Dynamical Systems