Henon Near-Crisis (a=1.43)

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What It Is

Henon map at a=1.43, b=0.3 --- just past the boundary crisis (~1.427) where the attractor has become a chaotic saddle: orbits stay chaotic for a long transient (~300 steps) then escape, so the emitted signal is a train of transient-chaos bursts separated by re-injection

Interpretation

Standard analysis sees: heavy-tailed; left-skewed; time-irreversible (slow rise, sharp collapse). The atlas additionally detects discrete-map sensitive dependence, Time Reversibility:ordinal_reversal_distance. It sits beside Zipf Distribution in the atlas (standard-bank rank 65) — a neighbor conventional features miss.

What standard analysis sees

tail heaviness0.88

asymmetry0.01

occupancy0.36

short-range corr0.19

long-range memory0.42

spectral colour0.63

periodicity0.21

complexity0.43

time-irreversibility0.10

volatility clustering0.45

multifractality0.46

dimensionality0.77

nonstationarity0.51

What the atlas adds

discrete-map sensitive dependence+3.5z

deterministic chaos (positive λ_max, sensitive dependence)

names a discrete-map-scoped estimate, NOT chaos in general — continuous-flow chaos (Lorenz, Rössler) reads weak/neutral here despite being genuinely chaotic; spiky arithmetic sources can false-positive on the finite-time estimate

Time Reversibility:ordinal_reversal_distance+2.5z

time-reversal symmetry breaking via Bandt-Pompe ordinal patterns

Atlas-extreme metrics the standard bank can’t predict for this source

Hölder Regularity:alpha_autocorrelation +3.3z bank-miss 1.2σ