peak FTLE kurtosis occurs near K=0.5 with value 138.157 +/- 1.953, while at the nominal critical region ftle_at_Kc is 0.04558 +/- 0.00007, var_at_Kc is 0.004054 +/- 0.000008, skew_at_Kc is 1.31990 +/- 0.00277, and frac chaotic rises from 0.00002 +/- 0.00001 at K=0.2 to 0.46210 +/- 0.00069 at K=1 and 0.98108 +/- 0.00016 at K=5.
The FTLE statistics resolve a sharp transition from mostly regular motion to overwhelmingly chaotic dynamics. The enormous low-K kurtosis peak shows that the onset region is dominated by rare extreme-stretch events and highly non-Gaussian finite-time fluctuations before chaos fills most trajectories. Once K increases past the transition window, the chaotic fraction saturates rapidly and the distribution narrows toward a more conventional chaotic regime. The implication is that kurtosis is a sensitive early-warning marker for the transition, preceding full occupancy of phase space by chaotic orbits.
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