Hamiltonian Systems 1
A.Y. 2018/2019
Learning objectives
1. The Hamiltonian formulation of Mechanics.
2. Introduction to perturbation theory for nearly integrable Hamiltonian systems.
2. Introduction to perturbation theory for nearly integrable Hamiltonian systems.
Expected learning outcomes
1. A basic knowledge of Hamiltonian formalism.
2. The main thorems on dynamics of Hamiltonian systems, proved during the last 50 years.
3. The methods of Hamiltonia perturbation theory.
2. The main thorems on dynamics of Hamiltonian systems, proved during the last 50 years.
3. The methods of Hamiltonia perturbation theory.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
Hamiltonian System 1 (first part)
Course syllabus
1. Hamiltonian formalism: Hamilton's equations; first integrals and Poisson brackets; canonical transformations; Hamilton-Jacoby equation.
2. Integrable systems: Liouville's theorem; Arnold-Jost theorem; equilibria in Hamiltonian systems; Kepler's problem.
3. Nearly integrable systems: dynamics in a neighbourhood of an elliptic equilibrium; Poincare's theorem; Lindtedt's method.
4. Near the identity canonical transformations: Lie series method, format and quantitative theory; normal form methods.
5. Kolmogorov's theorem on persistence of invariant tori.
6. The therome of Nekhoroshev on exponential stability.
7. Numerical methods in dynamics.
2. Integrable systems: Liouville's theorem; Arnold-Jost theorem; equilibria in Hamiltonian systems; Kepler's problem.
3. Nearly integrable systems: dynamics in a neighbourhood of an elliptic equilibrium; Poincare's theorem; Lindtedt's method.
4. Near the identity canonical transformations: Lie series method, format and quantitative theory; normal form methods.
5. Kolmogorov's theorem on persistence of invariant tori.
6. The therome of Nekhoroshev on exponential stability.
7. Numerical methods in dynamics.
Hamiltonian System 1 (first part)
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 42 hours
Professors:
Giorgilli Antonio, Sansottera Marco
Hamiltonian System 1 mod/02
MAT/07 - MATHEMATICAL PHYSICS - University credits: 3
Laboratories: 24 hours
Lessons: 7 hours
Lessons: 7 hours
Professors:
Giorgilli Antonio, Sansottera Marco