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Orbital Complexity, Short‐Time Lyapunov Exponents, and Phase Space Transport in Time‐Independent Hamiltonian Systems a
Author(s) -
SIOPIS CHRISTOS,
ECKSTEIN BARBARA L.,
KANDRUP HENRY E.
Publication year - 1998
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1998.tb11249.x
Subject(s) - lyapunov exponent , phase space , chaotic , mathematics , statistical physics , hamiltonian (control theory) , fourier transform , spectral density , spectral line , orbit (dynamics) , hamiltonian system , physics , mathematical analysis , quantum mechanics , nonlinear system , statistics , computer science , mathematical optimization , artificial intelligence , engineering , aerospace engineering
ABSTRACT: This paper compares two alternative characterizations of chaotic orbit segments, one based on the complexity of their Fourier spectra, as probed by the number of frequencies n ( k ) required to capture a fixed fraction k of the total power, and the other based on the computed values of short‐time Lyapunov exponents χ. An analysis of orbit ensembles evolved in several different two‐ and three‐dimensional potentials reveals that there is a strong, roughly linear correlation between these alternative characterizations, and that computed distributions of complexities, N [ n ( k )], and short‐time χ, N [χ], often assume similar shapes. This corroborates the intuition that chaotic segments which are especially unstable should have Fourier spectra with particularly broad‐band power. It follows that orbital complexities can be used as probes of phase space transport and other related phenomena in the same manner as can short‐time Lyapunov exponents.