ROTATION VECTORS AND ENTROPY FOR HOMEOMORPHISMS OF THE TORUS ISOTOPIC TO THE IDENTITY
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 0143-3857Full text not available from this repository.
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'.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||ERGODIC THEORY AND DYNAMICAL SYSTEMS|
|Publisher:||CAMBRIDGE UNIV PRESS|
|Official Date:||March 1991|
|Number of Pages:||14|
|Page Range:||pp. 115-128|
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