Integrability and chaos: the classical uncertainty

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now referred to as deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical mechanics. Based on the Hamiltonian formalism, the main objective of this paper is to provide, from the physicist's point of view, an overall and intuitive review of this broad subject (with some emphasis on the Kolmogorov-Arnold-Moser theorem and the stability of planetary motions) which may be useful to both students and instructors.