Journal
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume 107, Issue 4, Pages 1173-1241Publisher
WILEY
DOI: 10.1112/jlms.12710
Keywords
-
Categories
Ask authors/readers for more resources
In this study, we establish the relationship between the genus and possible geometries for homological rotation sets of maps on closed oriented surfaces with a genus g >= 2. We demonstrate that this invariant for Smale diffeomorphisms can be described as the union of at most 2(5g-3) convex sets, all containing zero. By utilizing the theory of hyperbolic dynamics, we extend this bound to a C-0-open and dense set of homeomorphisms, indicating its general validity. Additionally, we provide examples that illustrate the sharpness of this asymptotic order.
Searching for a relation between the genus g >= 2 of a closed oriented surface and the possible geometries for homological rotation sets of its maps, we prove that this invariant for Smale diffeomorphisms is given by a union of at most 2(5g-3) convex sets, all of them containing zero. The classical theory of hyperbolic dynamics allows then to extend this bound to a C-0-open and dense set of homeomorphisms, suggesting this to be a general fact. Examples showing the sharpness for this asymptotic order are provided.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available