 Escape-rate Green function of a polynomial

ID: escape-rate-green-function-of-a-polynomial

G_{f} (z) = lim_{n \to \infty} d^{- n} lo g^{+} ∣ f^{n} (z) ∣.

It vanishes on the filled Julia set, is positive and harmonic on the basin of infinity, satisfies

G_{f} \circ f = d G_{f}

, and equals

lo g ∣ ϕ_{f} ∣

near infinity and by continuation throughout the basin.

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