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Perturbations of flexible Lattès maps. (Perturbations des exemples de Lattès flexibles.) (English. French summary) Zbl 1326.37035
A rational map of degree $$D\geq 2$$ is strictly postcritically finite if the orbit of each critical point intersects a repelling cycle. A flexible Lattès map is a map $$f:\hat{\mathbb{C}}\to\hat{\mathbb{C}}$$ which is double-covered by an integral torus endomorphism, that is an endomorphism of the Riemann sphere such that there exists a $$2$$-to-$$1$$ cover $$\Theta:T\to \hat{\mathbb{C}}$$ from a torus $$T=\mathbb{C} / \Lambda$$ such that the pull-back of $$f$$ by $$\Theta$$ is an endomorpism $$L$$ of $$T$$ of the form $$L(\tau)=a\tau+b\pmod{\Lambda}$$ for an integer $$a$$. Such morphisms constitute examples of maps with Julia sets which are the entire Riemann sphere.