Introduction to dynamical systems II

Period of duration of course
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Course info
Number of course hours
20
Number of hours of lecturers of reference
20
Number of hours of supplementary teaching
0
CFU 3
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Type of exam

Oral exam

Lecturer

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Prerequisites

Introduzione ai sistemi dinamici I

Programme

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. 

 

Educational aims

The goal of the course is to introduce the fundamental
notions of the modern theory of dynamical systems.

Bibliographical references

Appunti distribuiti agli studenti. 

Beardon: Iteration of Rational Functions

Devaney: An Introduction To Chaotic Dynamical Systems