Skew product maps related to finitely generated rational semigroups

By Hiroki Sumi. 2000

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Semigroup Actions of Expanding Maps (2016, methodology): “The transfer operator L̂a,φ is precisely the averaged normalized transfer operator introduced in [26].”
Random complex dynamics and semigroups of holomorphic maps (2008, unknown): “Then, there exists a unique f -invariant ergodic Borel probability measure μ on Γ × Ĉ such that π∗(μ) = τ̃ and hμ(f |σ) = maxρ∈E1(ΓN×Ĉ):f∗(ρ)=ρ,π∗(ρ)=τ̃ hρ(f |σ) = ∑m j=1 pj log(deg(hj)), where hρ(f |σ) denotes the relative metric entropy of (f, ρ) with respect to (σ, τ̃ ), and E1(·) denotes the spa”
Semi-hyperbolic fibered rational maps and rational semigroups (2005, background): “J(f)) = J(G) (See Section 1.2 and [ S5 ]) is not equal to the Riemann sphere.”