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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

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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
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:
DateEvent
1991Published
29 October 1990Submitted
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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