| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Dept Matemat Aplicada, Inst Matemat & Estat, Sao Paulo - Brazil
[2] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | FUNDAMENTA MATHEMATICAE; v. 227, n. 1, p. 1-19, 2014. |
| Web of Science Citations: | 0 |
| Abstract | |
Let f : S-1 x {[}0, 1] -> S-1 x {[}0, 1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift (f) over tilde : R x {[}0, 1] -> R x {[}0, 1] we have Fix((f) over tilde) = R x [0] and that (f) over tilde positively translates points in R x [1]. Let (f) over tilde (is an element of) be the perturbation of (f) over tilde by the rigid horizontal translation (x, y) -> (x+is an element of, y). We show that Fix((f) over tilde (is an element of)) = empty set for all is an element of > 0 sufficiently small. The proof follows from Kerekjarto's construction of Brouwer lines for orientation preserving homeomorphisms of the plane with no fixed points. This result turns out to be sharp with respect to the regularity assumption: there exists a diffeomorphisra f with all the properties above, except that f is not real-analytic but only smooth, such that the above conclusion is false. Such a map is constructed via generating functions. (AU) | |
| FAPESP's process: | 11/16265-8 - Low dimensional dynamics |
| Grantee: | Edson Vargas |
| Support Opportunities: | Research Projects - Thematic Grants |