Instability statistics and mixing rates.

@article{Artuso2009InstabilitySA,
  title={Instability statistics and mixing rates.},
  author={Roberto Artuso and Cesar Manchein},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2009},
  volume={80 3 Pt 2},
  pages={
          036210
        }
}
  • R. Artuso, C. Manchein
  • Published 3 June 2009
  • Mathematics, Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We claim that looking at probability distributions of finite time largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincaré recurrences in the-quite-delicate case of dynamical systems with weak chaotic properties. 

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References

SHOWING 1-10 OF 48 REFERENCES
Large deviations for intermittent maps
In this paper we study large deviation results for the Manneville-Pomeau map and related transformations to indifferent fixed points. In particular, we consider conditions under which the associated
Anomalous transport : foundations and applications
In Memoriam: Radu Balescu Part I FRACTIONAL CALCULUS AND STOCHASTIC THEORY Threefold Introduction to Fractional Derivatives (Rudolf Hilfer) Random Processes with Infinite Moments (Michael F.
Proc.Amer.Math.Soc
  • Proc.Amer.Math.Soc
  • 2009
and G
  • Cristadoro, Phys.Rev. E 77, 046206
  • 2008
Phys
  • Rev. A 43, 3146
  • 1991
  • 2009
  • 2008
Large deviations for intermittent maps (unpublished)
  • Large deviations for intermittent maps (unpublished)
  • 2008
Phys.Rev. E
  • Phys.Rev. E
  • 2008
...
1
2
3
4
5
...