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

Publication ,  Journal Article
Charbonneau, P; Li, YC; Pfister, HD; Yaida, S
Published in: Physical review. E
September 2017

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.

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Published In

Physical review. E

DOI

EISSN

2470-0053

ISSN

2470-0045

Publication Date

September 2017

Volume

96

Issue

3-1

Start / End Page

032129

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
 

Citation

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Charbonneau, P., Li, Y. C., Pfister, H. D., & Yaida, S. (2017). Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments. Physical Review. E, 96(3–1), 032129. https://doi.org/10.1103/physreve.96.032129
Charbonneau, Patrick, Yue Cathy Li, Henry D. Pfister, and Sho Yaida. “Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments.Physical Review. E 96, no. 3–1 (September 2017): 032129. https://doi.org/10.1103/physreve.96.032129.
Charbonneau P, Li YC, Pfister HD, Yaida S. Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments. Physical review E. 2017 Sep;96(3–1):032129.
Charbonneau, Patrick, et al. “Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments.Physical Review. E, vol. 96, no. 3–1, Sept. 2017, p. 032129. Epmc, doi:10.1103/physreve.96.032129.
Charbonneau P, Li YC, Pfister HD, Yaida S. Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments. Physical review E. 2017 Sep;96(3–1):032129.

Published In

Physical review. E

DOI

EISSN

2470-0053

ISSN

2470-0045

Publication Date

September 2017

Volume

96

Issue

3-1

Start / End Page

032129

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering