On $DA$-endomorphisms of the two-dimensional torus

It is proved that in each homotopy class of continuous mappings of the two-dimensional torus to itself that induce a hyperbolic action on the fundamental group, as long as it is free of expanding mappings, there exists an $A$-endomorphism $f$ whose nonwandering set consists of an attracting hyperbolic sink and a nontrivial one-dimensional collapsing repeller, which is a one-dimensional orientable lamination, locally homeomorphic to the direct product of a Cantor set and a line segment. Moreover, the unstable $Df$-invariant subbundle of the tangent space to the repeller has the property of uniqueness.
Bibliography: 23 titles.