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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

New rotation sets in a family of torus homeomorphisms

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Author(s):
Boyland, Philip [1] ; de Carvalho, Andre [2] ; Hall, Toby [3]
Total Authors: 3
Affiliation:
[1] Univ Florida, Dept Math, 372 Little Hall, Gainesville, FL 32611 - USA
[2] Univ Sao Paulo, IME, Dept Matemat Aplicada, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
[3] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside - England
Total Affiliations: 3
Document type: Journal article
Source: INVENTIONES MATHEMATICAE; v. 204, n. 3, p. 895-937, JUN 2016.
Web of Science Citations: 6
Abstract

We construct a family of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation set bifurcations and prevalence. We show that there is a full measure subset of {[}0, 1], consisting of infinitely many mutually disjoint non-trivial closed intervals, on each of which the rotation set mode locks to a constant polygon with rational vertices; that the generic rotation set in the Hausdorff topology has infinitely many extreme points, accumulating on a single totally irrational extreme point at which there is a unique supporting line; and that, although varies continuously with t, the set of extreme points of does not. The family also provides examples of rotation sets for which an extreme point is not represented by any minimal invariant set, or by any directional ergodic measure. (AU)

FAPESP's process: 10/09667-0 - Topological methods in low-dimensional dynamics
Grantee:André Salles de Carvalho
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 11/17581-0 - Topological methods in surface dynamics: from the Hénon family to torus rotation sets
Grantee:André Salles de Carvalho
Support type: Research Grants - Visiting Researcher Grant - International