A Review of the “Third” integral

George Contopoulos

doi:10.3934/mine.2020022

Mathematics in Engineering, 2020, 2(3): 472-511. doi: 10.3934/mine.2020022. Review Special Issues

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A Review of the “Third” integral

George Contopoulos

Research Center for Astronomy of the Academy of Athens Soranou Efesiou 4, Athens, GR- 11527, Greece

^†This contribution is part of the Special Issue: Modern methods in Hamiltonian perturbation theory
Guest Editors: Marco Sansottera; Ugo Locatelli
Link: http://www.aimspress.com/newsinfo/1356.html

Received: , Accepted: , Published:

Special Issues: Modern methods in Hamiltonian perturbation theory

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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.

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Keywords: integrals of motion; resonances; density waves; orbits in relativity and cosmology; classical and quantum chaos

Citation: George Contopoulos. A Review of the “Third” integral. Mathematics in Engineering, 2020, 2(3): 472-511. doi: 10.3934/mine.2020022

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