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Minimal periodic orbit structure of 2-dimensional homeomorphisms

Solari, HG and Natiello, Mario LU (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.
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author
organization
publishing date
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
2007-08-20 09:37:14
date last changed
2017-03-14 13:42:24
@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},
  keyword      = {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},
  volume       = {15},
  year         = {2005},
}