Continuation of normal doubly symmetric orbits in conservative reversible systems

Details Continuation of normal doubly symmetric orbits in conservative reversible systems Continuation of normal doubly symmetric orbits in conservative reversible systems

Jan 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cemda..97...17m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 97, Issue 1, pp.17-47

Astronomy and Astrophysics

Astronomy

2

Scientific paper

In this paper we introduce the concept of a quasi-submersive mapping between two finite-dimensional spaces, we obtain the main properties of such mappings, and we introduce “normality conditions” under which a particular class of so-called “constrained mappings” are quasi-submersive at their zeros. Our main application is concerned with the continuation properties of normal doubly symmetric orbits in time-reversible systems with one or more first integrals. As examples we study the continuation of the figure-eight and the supereight choreographies in the N-body problem.

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