Category: Nonlinear Dyn.

Summary: Measuring how the finite-time Lyapunov-exponent distribution changes across the chaos transition of the Chirikov standard map.

The Chirikov standard map is a benchmark model for the onset of Hamiltonian chaos. This experiment asks not only where chaotic behavior appears, but how the full distribution of finite-time Lyapunov exponents changes near the transition where sticky motion near surviving regular structures still matters.

The simulation sweeps the kick strength across the regular-to-chaotic crossover and records Lyapunov exponents over finite observation windows. The target is a distributional picture: heavy tails and slow variance decay would indicate that sticky trajectories near KAM remnants continue to shape finite-time predictability even after chaos has begun to spread.

That emphasis on the full distribution is the interesting part. Rather than reducing the transition to a single mean exponent, the experiment asks how intermittency and anomalous tangent-space diffusion appear in the statistics of finite-time instability.

Method: Repeated standard-map simulations across kick strengths, measuring finite-time Lyapunov exponents and their full distributions over different observation times.

What is measured: Finite-time Lyapunov-exponent distribution, mean and variance of FTLEs, tail heaviness or kurtosis, and dependence on kick strength and observation time.