Hamiltonian perturbation theory

Summary

Hamiltonian perturbation theory studies systems whose Hamiltonian is a small perturbation $H_0 + \varepsilon H_1$ of an integrable one $H_0$. It looks for canonical transformations close to the identity that remove the dependence on the angles order by order in $\varepsilon$. These are usually built from a generating function. The method meets the problem of small divisors, which comes from resonances between the frequencies of the unperturbed motion. Controlling these small divisors is the core of the Kolmogorov–Arnold–Moser theorem. See the definition.