A BRANCHED COVERING OF DEGREE 2 OF THE SPHERE WITH A COMPLETELY INVARIANT INDECOMPOSABLE CONTINUUM.

The paper explicitly constructs a degree‑2 branched covering F:S^2→S^2 via a Lattès-type quotient of a hyperbolic toral endomorphism and a local derived-from-Anosov modification at two fixed points; the complement K of the two attracting basins is a hyperbolic repeller, locally Cantor×interval, with dense leaves, hence indecomposable (Theorem 2) . The candidate solution follows the same blueprint (torus endomorphism A, quotient by x∼−x, symmetric modification, completely invariant basins, K locally Cantor×I with dense leaf), differing mainly in modifying on the torus before descending rather than modifying on the sphere; the paper later notes the constructed F lifts to the torus, making the two approaches essentially equivalent .