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On the rank-one limit sets for maps in the constant-Jacobian shear group of $\mathbb{C}^2$
Let $\mathcal{S}_c$ be the subgroup of $Aut(\mathbb{C}^2)$ generated by affine maps and shear automorphisms with constant Jacobian. We determine the possible conformal types of the rank-one limit set of an invariant recurrent Fatou component when the induced dynamics has infinite order. In particula
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