Natural Invariant Measure (SRB Measure)

The natural measure μ is what a typical orbit spends its time visiting. For chaotic attractors, this is the Sinai-Ruelle-Bowen (SRB) measure — unique, physically meaningful.

SRB (1970s): For Axiom A systems, the SRB measure is the unique invariant measure absolutely continuous along unstable manifolds. μ(A) = fraction of time a generic orbit spends in A (Birkhoff ergodic theorem).
Map and cobweb (first 80 steps)
Empirical invariant measure μ vs exact ρ
Lyapunov λ: —   KS entropy h: —   Pesin identity (h=λ): —
Time series x(n) — first 500 iterates
Click "Compute Measure" to generate the SRB measure empirically.