On the existence of an entropy-like quantity

Details On the existence of an entropy-like quantity On the existence of an entropy-like quantity

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983ap%26ss..96..227e&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 96, no. 1, Oct. 1983, p. 227-229.

Astronomy and Astrophysics

Astrophysics

Celestial Mechanics, Entropy, Ergodic Process, Orbits, Geodesy, Poincare Problem

Scientific paper

An analytical study of the orbits of a dynamical system using topological methods is presented. The existence of the entropylike quantity k introduced by Benettin et al. (1976) is considered, based on the observation that the quantity k(n), related to interorbit distance, can be linked with the Gaussian curvature of the dynamical system by referring it to the distance between neighboring geodesics. It is found that k definitely exists for manifolds with positive Gaussian curvature and may exist for negative manifolds as well when the curvature is not a constant. The importance of k is seen in its usefulness in studying the ergodicity of the system components and hence the integrability of systems like that of Henon and Heiles (1963). The Euler-Poincare characteristic of systems in which k is an extremum along the geodesic is found to be zero.

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