Quartic polynomial approximation for fluctuations of separation of trajectories in chaos and correlation dimension

@article{Fouxon2019QuarticPA,
  title={Quartic polynomial approximation for fluctuations of separation of trajectories in chaos and correlation dimension},
  author={Itzhak Fouxon and Siim Ainsaar and Jaan Kalda},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2019},
  volume={2019}
}
We consider the cumulant generating function of the logarithm of the distance between two infinitesimally close trajectories of a chaotic system. Its long-time behavior is given by the generalized Lyapunov exponent providing the logarithmic growth rate of the kth moment of the distance. The Legendre transform of is a large deviations function that gives the probability of rare fluctuations where the logarithmic rate of change of the distance is much larger or much smaller than the mean rate… 

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