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ROTATION VECTORS AND ENTROPY FOR HOMEOMORPHISMS OF THE TORUS ISOTOPIC TO THE IDENTITY
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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.
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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'.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Journal or Publication Title: | ERGODIC THEORY AND DYNAMICAL SYSTEMS | ||||
| Publisher: | CAMBRIDGE UNIV PRESS | ||||
| ISSN: | 0143-3857 | ||||
| Official Date: | March 1991 | ||||
| Dates: |
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| Volume: | 11 | ||||
| Number: | Part 1 | ||||
| Number of Pages: | 14 | ||||
| Page Range: | pp. 115-128 | ||||
| Publication Status: | Published |
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