On Latt\`es Maps

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Foliations of Hilbert modular surfaces (2007, background): “It is well-known that the Julia set of any Latt` es example is the whole Riemann sphere; and that in any stable family, the Julia set varies by a holomorphic motion respecting the dynamics (see e.g. [MSS], [Mc1, Ch. 4], [ Mil ].)”
Bifurcation currents in holomorphic dynamics on ${\bf P}^k$ (2005, background): “ular any non-ﬂexible Latt`es map lies in the support of µ. Proof. For d≥ 2 ﬁxed, let f0 ∈ Hd(P1) be a non-ﬂexible Latt`es map (e.g. f0 is the map associated to an imaginary quadratic number ﬁeld, see [22] Lemma 5.4), then all Latt`es maps which belong to a small neighbourhood of f0 in Hd(P1) are con”