Conformal Fractals: Ergodic Theory Methods

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Shadowing and $\omega $-limit sets of circular Julia sets (2011, methodology): “The following property (for the case Λ = X) was introduced implicitly in [23] in the proof that expanding open maps have shadowing.”
Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory (2008, unknown): “ the statement of the theorem. Recall that ξˆ −n increases to ξˆu. Hence for ˆµa.e. ˆp and every measurable function ψ, ˆµξˆ −n(ˆp) (ψ) → µˆξˆu(ˆp)(ψ) (this is the Martingale Convergence Theorem, see [PU]). Now if ψis of the form ϕ◦π0, the statement that (π0)∗µˆˆξ −n(ˆp) = ˇµξ(π 0(ˆp)), implies that”