Programme

Trottola di Lagrange. Trasformazione canoniche. Parentesi di Poisson e condizione di Lie. Funzioni generatrici. Teoria delle perturbazioni. Equazione omologica. Sistemi iscocroni e anisocroni. Serie di Birkhoff. Teoria perturbativa a tutti gli ordini per sistemi isocroni e teorema di Nekhoroshev. Teorema KAM.

Core Documentation

G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, available online
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online

Reference Bibliography

V.I. Arnol’d, Mathematical Methods of Classical Mechanics, Springer (1989). A. Fasano & S. Marmi, Analytical Mechanics, Oxford University Press (2006). G. Gallavotti, The Elements of Mechanics, Springer (1983). L.D. Landau & E.M. Lifshitz, Mechanics, Pergamon Press (1960).

Type of delivery of the course

Lectures. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

Attendance

Attending the course is strongly recommended but not mandatory.

Type of evaluation

The exam consists of an oral interview in which the student will have to discuss the topics covered in class, with reference to the texts used and/or the notes distributed in class. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]