Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments.

Journal Article (Journal Article)

Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical ζ function for one-dimensional systems. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the ζ function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance and is tested against Monte Carlo simulations.

Full Text

Duke Authors

Cited Authors

  • Charbonneau, P; Li, YC; Pfister, HD; Yaida, S

Published Date

  • September 18, 2017

Published In

Volume / Issue

  • 96 / 3-1

Start / End Page

  • 032129 -

PubMed ID

  • 29346975

Electronic International Standard Serial Number (EISSN)

  • 2470-0053

International Standard Serial Number (ISSN)

  • 2470-0045

Digital Object Identifier (DOI)

  • 10.1103/physreve.96.032129


  • eng