Sensitivity, entropy, and escape rates at the onset of chaos

Details Sensitivity, entropy, and escape rates at the onset of chaos Sensitivity, entropy, and escape rates at the onset of chaos

2011-06-19

arxiv.org/abs/1106.3761v1

Physics

Condensed Matter

Statistical Mechanics

7 pages including 2 figures. Phys. Lett. A (2011), in press

Scientific paper

10.1016/j.physleta.2011.06.039

We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in $z$-logistic maps for both positive and zero Lyapunov exponents. We unify these relations at chaos, where the Lyapunov exponent is positive, and at its onset, where it vanishes. Our result unifies, in particular, two already known cases, namely (i) the standard entropy rate in the presence of escape, valid for exponential functionality rates with strong chaos, and (ii) the Pesin-like identity with no escape, valid for the power-law behavior present at points such as the Feigenbaum one.

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