Rotational chaos and strange attractors on the 2-torus

We construct a 2-torus homeomorphism \(h\) homotopic to the identity with an attracting R. H. Bing’s pseudocircle \(C\) such that the rotation set of \(h|C\) is not a unique vector. The only known examples of such an attractor were Birkhoff’s attractors, arising for dissipative maps with a twist. Our construction relies heavily on the Barge–Martin method for constructing attractors as inverse limits of graphs.