Perturbation Theory

Abstract

Given the Hamiltonian H ₀ of a completely integrable system, the perturbed problem is described by the Hamiltonian H = H ₀ + εHp, where Hp is a function whose numerical value is of the same order of H ₀, and ε << 1. The perturbed problem thus differs slightly from the unperturbed one, but unfortunately the same is not true for the solution: a small perturbation can give rise to secular effects, i.e., to a slow but progressive wandering from the unperturbed, and known for infinite time, solution.

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