Mathematics – Probability
Scientific paper
Oct 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57..123f&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 1-2, p. 123-130
Mathematics
Probability
Hamiltonian Functions, Liapunov Functions, Mapping, Orbit Calculation, Poincare Problem, Celestial Mechanics, Probability Theory
Scientific paper
Poincare maps for Hamiltonian systems with 3 degrees of freedom lead to the study of four dimensional symplectic mappings. As a test for the validity of a synthetic mapping of order 3 using gradient informations, we study the evolution with time of Liapounov Indicators in the case of the four dimensional standard map with chaotic and stable zones. Both Liapounov Indicators show the same behaviour for the real and synthetic mappings. They reveal exploding diffusion phenomena for temporarily confined chaotic orbits. The distribution of the time of explosion fits well with a Poisson law for the real mapping, but not for the synthetic one. However, the mean time of explosion is essentially the same in both cases.
Froeschlé Ch.
Petit Jean-Marc
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