Integrability and chaos: the classical uncertainty

TL;DR

This paper provides an intuitive review of classical chaos and integrability, emphasizing Hamiltonian formalism, KAM theorem, and planetary stability, aimed at students and educators in physics.

Contribution

It offers a comprehensive, accessible overview of deterministic chaos and integrability from a physicist's perspective, including key concepts like the KAM theorem.

Findings

Emphasizes the importance of Hamiltonian formalism in understanding chaos.

Highlights the role of the KAM theorem in planetary motion stability.

Provides educational insights for students and instructors in classical mechanics.

Abstract

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 named by the more fashionable term of 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 article is to provide, from the physicist's point of view, an overall and intuitive review of this broad subject (with some emphasis on the KAM theorem and the stability of planetary motions) which may be useful to both students and instructors.