| Full text | |
| Author(s): |
Boyland, Philip
[1]
;
de Carvalho, Andre
;
Hall, Toby
Total Authors: 3
|
| Affiliation: | [1] Univ Florida, Dept Math, Gainesville, FL 32611 - USA
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | GEOMETRY & TOPOLOGY; v. 25, n. 1, p. 111-228, 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
Let [f(t): I -> I] be a family of unimodal maps with topological entropies h(f(t)) > 1/2 log 2, and (f) over cap (t) : (I) over cap (t) -> (I) over cap (t) be their natural extensions, where (I) over cap (t) = (sic) (I, f(t)). Subject to some regularity conditions, which are satisfied by tent maps and quadratic maps, we give a complete description of the prime ends of the Barge-Martin embeddings of (I) over cap (t) into the sphere. We also construct a family [chi(t) : S-2 -> S-2] of sphere homeomorphisms with the property that each chi(t) is a factor of (f) over cap (t), by a semiconjugacy for which all fibers except one contain at most three points, and for which the exceptional fiber carries no topological entropy; that is, unimodal natural extensions are virtually sphere homeomorphisms. In the case where [f(t)] is the tent family, we show that chi(t) is a generalized pseudo-Anosov map for the dense set of parameters for which f(t) is postcritically finite, so that [chi(t)] is the completion of the unimodal generalized pseudo-Anosov family introduced by de Carvalho and Hall (Geom. Topol. 8 (2004) 1127-1188). (AU) | |
| FAPESP's process: | 16/04687-9 - Dynamics and geometry in dimensions 1, 2 and 3 |
| Grantee: | André Salles de Carvalho |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 11/16265-8 - Low dimensional dynamics |
| Grantee: | Edson Vargas |
| Support Opportunities: | Research Projects - Thematic Grants |