How to Extract Regularity from Disguised Irregular Levels of Integrable Hamiltonian System

Abstract

The eigenvalues of an integrable hamiltonian of two degrees of freedom can be expressed as E(n, m) with n, m integers. Although E(n, m) are regular with respect to n (or m) when m (or n) is held fixed, the sequence of E(n, m) arranged in the order of magnitude looks irregular. We want to give an algorithm for extracting regularity from the level spacings or the energy levels with disguised irregularities in an integrable system. Further a method is proposed to distinguish true irregularities in non-integrable system from disguised ones in integrable system.