Constraint on periodic orbits of chaotic systems given by Random Matrix Theory

2010/12/29 by Alejandro G. Monastra, Monastra, Alejandro G.
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.CD

paper · pdf · doi:10.48550/arxiv.1012.5952

11 pages, no figures

arxiv created 2010/12/29 · arxiv updated 2010/12/30

Abstract

Considering the fluctuations of spectral functions, we prove that if chaotic systems fulfill the Bohigas-Gianonni-Schmit (BGS) conjecture, which relates their spectral statistics to that of random matrices, therefore by virtue of Gutzwiller trace formula, the instability of classical periodic orbits is constrained. In particular for two-dimensional chaotic systems, the Lyapunov exponent λ_p of each periodic orbit p should be bigger than a minimum value λ_min ≥ 0.850738. This opens the possibility of new constraints for a system to be fully chaotic, or the failure of the BGS conjecture.

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