Advanced

Remarks on Braid Theory and the characterisation of periodic orbits

Natiello, Mario LU and Solari, Hernan (1994) In Journal of Knot Theory and its Ramifications 3(4). p.511-529
Abstract
The relationship between Braid Theory and the organisation of periodic orbits of dynamical systems is considered.



It is shown that for some (physically relevant) 3-d flows the characterisation of periodic orbits by means of Braid Theory can be done on the Poincaré surface in an efficient way. The result is a thread-less graphical presentation of a braid class.



We discuss extensions of this approach to (adequate) dynamical systems of dimension higher than three, using results from Central Manifold Theory.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Knot Theory and its Ramifications
volume
3
issue
4
pages
511 - 529
publisher
World Scientific
ISSN
1793-6527
DOI
10.1142/S021821659400037X
language
English
LU publication?
yes
id
8ae23a08-6090-4daf-b0b7-ab6730f126c6 (old id 1263679)
alternative location
http://s021821659400037x.pdf/
date added to LUP
2008-12-08 10:12:08
date last changed
2017-03-14 13:42:26
@article{8ae23a08-6090-4daf-b0b7-ab6730f126c6,
  abstract     = {The relationship between Braid Theory and the organisation of periodic orbits of dynamical systems is considered.<br/><br>
<br/><br>
It is shown that for some (physically relevant) 3-d flows the characterisation of periodic orbits by means of Braid Theory can be done on the Poincaré surface in an efficient way. The result is a thread-less graphical presentation of a braid class.<br/><br>
<br/><br>
We discuss extensions of this approach to (adequate) dynamical systems of dimension higher than three, using results from Central Manifold Theory.},
  author       = {Natiello, Mario and Solari, Hernan},
  issn         = {1793-6527},
  language     = {eng},
  number       = {4},
  pages        = {511--529},
  publisher    = {World Scientific},
  series       = {Journal of Knot Theory and its Ramifications},
  title        = {Remarks on Braid Theory and the characterisation of periodic orbits},
  url          = {http://dx.doi.org/10.1142/S021821659400037X},
  volume       = {3},
  year         = {1994},
}