CAN POINTS OF BOUNDED ORBITS SURROUND POINTS OF UNBOUNDED ORBITS ?

The paper proves that for any disk E ⊂ R^2 there is a plane homeomorphism h with bounded orbits on ∂E and doubly divergent orbits on Int(E), via a construction on J^2 using normally rising homeomorphisms (Theorems 1.2 and 3.5) and a conjugacy pipeline employing a semi-conjugacy ξ, a coordinate blow-up ψ, and the Schönflies theorem ζ . The candidate solution gives a different, explicit construction: h = u ∘ T where T is a translation and u is a compactly supported shear inverse that fixes ∂E pointwise and leaves all interior orbits asymptotically like T in both time directions, hence doubly divergent. The argument is sound; minor technical points (e.g., support of u vs. j) are easily patched. Thus both the paper and the model are correct, with substantially different proofs.