The Lyapunov characteristic exponents - Applications to celestial mechanics

Details The Lyapunov characteristic exponents - Applications to celestial mechanics The Lyapunov characteristic exponents - Applications to celestial mechanics

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..34...95f&link_type=abstract

(Bundesministerium für Wissenschaft und Forschung of Austria, Alexander von Humboldt Colloquium on Celestial Mechanics: The Stab

Statistics

Computation

44

Celestial Mechanics, Liapunov Functions, Orbit Calculation, Ergodic Process, Hamiltonian Functions, Jacobi Matrix Method, Trajectory Analysis, Vector Analysis

Scientific paper

Liapunov characteristic exponent (LCEs) are introduced discussed in terms of the divergence of nearby orbits and the spectral properties of a linear operator. A simple example of a periodic orbit is explored and then generalized, and theoretical results of LCEs are presented with a special emphasis on Hamiltonian systems. The connection between Kolmogorov entropy and LCEs is given via Pesin's formula. Numerical techniques to compute LCEs are described, with special emphasis on the work of Benettin et al. (1980), and computations of LCEs in the context of celestial mechanics are reviewed.

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