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Typical recurrence for lifts of mean rotation zero annulus homeomorphisms
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Alpern, Steve and Prasad, Vidhu (1991) Typical recurrence for lifts of mean rotation zero annulus homeomorphisms. Bulletin of the London Mathematical Society, 23 (5). pp. 477-481. doi:10.1112/blms/23.5.477 ISSN 0024-6093 .
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Official URL: http://dx.doi.org/10.1112/blms/23.5.477
Abstract
This paper is about typical (uniform topology dense Gg) properties of homeomorphisms of the torus or annulus which preserve a fixed measure and have mean rotation zero. We first show that ergodicity is typical (Theorem 1). We then show that the lift (to the universal covering space) of such a homeomorphism of the annulus is the skew product of the annulus homeomorphism with respect to a skewing function of mean zero. Hence Atkinson's Theorem on skew products, together with Theorem 1, implies that it is typical for an annulus homeomorphism of mean rotation zero to have a recurrent lift (Theorem 3). Standard arguments then give the Poincare-Birkhoff Fixed Point Theorem as a corollary.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
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| Library of Congress Subject Headings (LCSH): | Homeomorphisms | ||||||
| Journal or Publication Title: | Bulletin of the London Mathematical Society | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 0024-6093 | ||||||
| Official Date: | 1991 | ||||||
| Dates: |
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| Volume: | 23 | ||||||
| Number: | 5 | ||||||
| Page Range: | pp. 477-481 | ||||||
| DOI: | 10.1112/blms/23.5.477 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | North Atlantic Treaty Organization (NATO) | ||||||
| Grant number: | 02451/89 (NATO) |
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