SINGULARITIES OF INTEGRABLE AND NEAR-INTEGRABLE HAMILTONIAN-SYSTEMS

The aim of this Letter is to show that the singularities of integrable Hamiltonian systems, besides being important for such systems themsel ves, also have many applications in the study of near-integrable syste ms. In particular, we will show how they are related to Kolmogorov's n ondegeneracy condition (in the famous KAM theorem), the Poincare-Melni kov function and its generalizations, topological entropy, and noninte grability criteria.