1 research outputs found
Dynamical estimates of chaotic systems from Poincar\'e recurrences
We show that the probability distribution function that best fits the
distribution of return times between two consecutive visits of a chaotic
trajectory to finite size regions in phase space deviates from the exponential
statistics by a small power-law term, a term that represents the deterministic
manifestation of the dynamics, which can be easily experimentally detected and
theoretically estimated. We also provide simpler and faster ways to calculate
the positive Lyapunov exponents and the short-term correlation function by
either realizing observations of higher probable returns or by calculating the
eigenvalues of only one very especial unstable periodic orbit of low-period.
Finally, we discuss how our approaches can be used to treat data coming from
complex systems.Comment: subm. for publication. Accepted fpr publication in Chao