UNSPECIFIED. (1991) ROTATION VECTORS AND ENTROPY FOR HOMEOMORPHISMS OF THE TORUS ISOTOPIC TO THE IDENTITY. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 11 (Part 1). pp. 115-128. ISSN 0143-3857

Abstract

We show that if a homeomorphism f of the torus, isotopic to the identity, has three or more periodic orbits with non-collinear rotation vectors, then it has positive topological entropy. Furthermore, for each point p of the convex hull DELTA of their rotation vectors, there is an orbit of rotation vector p, for each rotational point p/q, p is-a-member-of Z2, q is-an-element-of N, in the interior of DELTA, there is a periodic orbit of rotation vector p/q, and for every compact connected subset C of DELTA there is an orbit whose rotation set is C. Finally, we prove that f has 'toroidal chaos'.

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