Local Lyapunov exponents in chaotic systems
The notion of local Lyapunov exponents (LLE) for dynamical systems is defined in the paper both for the systems with continuous time and for whose with discrete time. The results of the computer calculations of the LLE for some systems are discussed. Calculations are presented for the dissipative Lorenz system, conservative Chirikov-Taylor map, and for a 3D volume preserving flow. The results demonstrate that large fluctuations of the LLE's around the long time average for an unstable trajectory take place.
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