Minimal periodic orbit structure of 2-dimensional homeomorphisms
(2005) In Journal of Nonlinear Science 15(3). p.183-222- Abstract
- We present a method for estimating the minimal periodic orbit structure, the topological entropy, and a fat representative of the homeomorphism associated with the existence of a finite collection of periodic orbits of an orientation-preserving homeomorphism of the disk D-2. The method focuses on the concept of fold and recurrent bogus transition and is more direct than existing techniques. In particular, we introduce the notion of complexity to monitor the modification process used to obtain the desired goals. An algorithm implementing the procedure is described and some examples are presented at the end.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/233031
- author
- Solari, HG and Natiello, Mario LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- pseudo-Anosov, Thurston classification theorem, 2-D homeomorphisms of the disk, topological entropy, minimal periodic orbit structure, representative
- in
- Journal of Nonlinear Science
- volume
- 15
- issue
- 3
- pages
- 183 - 222
- publisher
- Springer
- external identifiers
-
- wos:000230488900003
- scopus:84867935350
- ISSN
- 0938-8974
- DOI
- 10.1007/s00332-005-0637-1
- language
- English
- LU publication?
- yes
- id
- ab73b9ea-54fc-4ff6-83b8-3aa5fa8ba423 (old id 233031)
- date added to LUP
- 2016-04-01 11:51:50
- date last changed
- 2022-01-26 19:20:31
@article{ab73b9ea-54fc-4ff6-83b8-3aa5fa8ba423,
abstract = {{We present a method for estimating the minimal periodic orbit structure, the topological entropy, and a fat representative of the homeomorphism associated with the existence of a finite collection of periodic orbits of an orientation-preserving homeomorphism of the disk D-2. The method focuses on the concept of fold and recurrent bogus transition and is more direct than existing techniques. In particular, we introduce the notion of complexity to monitor the modification process used to obtain the desired goals. An algorithm implementing the procedure is described and some examples are presented at the end.}},
author = {{Solari, HG and Natiello, Mario}},
issn = {{0938-8974}},
keywords = {{pseudo-Anosov; Thurston classification theorem; 2-D homeomorphisms of the disk; topological entropy; minimal periodic orbit structure; representative}},
language = {{eng}},
number = {{3}},
pages = {{183--222}},
publisher = {{Springer}},
series = {{Journal of Nonlinear Science}},
title = {{Minimal periodic orbit structure of 2-dimensional homeomorphisms}},
url = {{http://dx.doi.org/10.1007/s00332-005-0637-1}},
doi = {{10.1007/s00332-005-0637-1}},
volume = {{15}},
year = {{2005}},
}