A Review of the “Third” integral

Abstract

We present the history of the third integral from a personal viewpoint. In particular, we mention the discovery of particular forms of the third integral, especially in resonant cases, the generation of chaos due to resonance overlap, the nonlinear theory of spiral density waves and applications in relativity and cosmology and in quantum mechanics. Finally we refer to some recent developments concerning the use of the third integral in finding chaotic orbits.

Keywords

• integrals of motion
• resonances
• density waves
• orbits in relativity and cosmology
• classical and quantum chaos