The Evolution of Periodic Orbits Close to Homoclinic Points

Details The Evolution of Periodic Orbits Close to Homoclinic Points The Evolution of Periodic Orbits Close to Homoclinic Points

Sep 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...8..273d&link_type=abstract

Celestial Mechanics, Volume 8, Issue 2, pp.273-280

Mathematics

Dynamical Systems

4

Scientific paper

For conservative dynamical systems having two degrees of freedom Birkhoff has established the existence of two classes of periodic orbits. The first consists of stable-unstable pairs close to periodic orbits of the stable type, and the second of orbits having fixed points (in a suitable surface of section) close to homoclinic points. In this paper orbits of the latter type are listed, and their evolution followed as a function of the energy. For the energy at which they were first computed, all were unstable; but they evolved, with diminishing energy, into one orbit of the stable type which appears to be a member of the first class of orbits mentioned above.

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