Lectures on integrable Hamiltonian systems

TL;DR

This paper discusses the theory of integrable Hamiltonian systems, including non-compact invariant submanifolds, with applications to systems like the Kepler problem and time-dependent Hamiltonians.

Contribution

It extends the theory of integrable Hamiltonian systems to include non-compact invariant submanifolds and non-autonomous systems.

Findings

General framework for non-compact invariant submanifolds

Application to the Kepler system

Analysis of time-dependent integrable systems

Abstract

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems with time-dependent parameters.