Sumários

Inverted pendulum

15 Novembro 2024, 16:00 • Ana Maria Ribeiro Ferreira Nunes

Brief discussion of the problem.

Perturbative methods and Hamiltonian systems

13 Novembro 2024, 16:00 • Ana Maria Ribeiro Ferreira Nunes

Parametric resonance. Arnold's tongues for the swing.

Hamiltonian systems and Liouville's theorem.
Integrable Hamiltonian sytems.
Liouville-Arnol'd's theorem.
KAM theorem.

Problems

8 Novembro 2024, 16:00 • Ana Maria Ribeiro Ferreira Nunes

Problems on Poincaré's compactification and analytic solution of the pendulum.

Perturbative methods

6 Novembro 2024, 16:00 • Ana Maria Ribeiro Ferreira Nunes

Lindsted-Poincaré method. Multiscale pertubative methods.

Krylov–Bogolyubov method of averaging

Methods for periodic orbits.

30 Outubro 2024, 16:00 • Ana Maria Ribeiro Ferreira Nunes

Topological methods: Poincaré's compactification.

Analytic methods: introduction to perturbation theory.