Fully Chaotic Conservative Models for Some Torus Homeomorphisms

The uploaded paper proves the existence of a monotone semiconjugate factor g with the same rotation set as f, which is (up to conjugacy) area-preserving, topologically mixing (and whose lift is mixing when 0 is in the interior of the rotation set), infinitely continuum-wise expansive, tight, and has Markovian horseshoes in every open set, exactly as stated in Theorem A. The proof is built via a new dynamically bounded equivalence relation and a quotient (the essential factor), uses a new uniform-unboundedness criterion (Theorem C), establishes mixing (Proposition 7.1 and Theorem D), constructs horseshoes densely (Proposition 9.1), and invokes Oxtoby–Ulam to get a conservative model (Proposition 10.1). These results directly contradict the candidate model’s claim that the statement was likely still open as of the cutoff. The paper’s argument appears coherent and complete, though it has a minor presentational slip where “Per(g) = T^2” should read “Per(g) dense in T^2.”