Stable chaos and local integrals of motion

Details Stable chaos and local integrals of motion Stable chaos and local integrals of motion

Nov 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002esasp.500..355v&link_type=abstract

In: Proceedings of Asteroids, Comets, Meteors - ACM 2002. International Conference, 29 July - 2 August 2002, Berlin, Germany. Ed

Mathematics

Logic

Asteroids, Stable Chaos, Local Integrals

Scientific paper

In previous publications we suggested that stable chaos is related to the existence of local integrals of motion in the phase-space region occupied by the trajectory. In order to test this hypothesis we estimated, using a numerical method, the topological dimension, d3, of several trajectories in the 3-D embedding space of proper elements. Our first results show that, while chaotic orbits may have 1 ≤ d3 ≤ 3 (regular orbits have d3 = 0), stable-chaotic orbits typically have d3 = 1. Thus stable-chaos can be associated with the near-conservation of 2 local integrals of motion.

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