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A Braided View of a Knotty Story

Natiello, Mario LU and Solari, Hernán G (2013) In Topology and Dynamics of Chaos p.149-168
Abstract
Periodic orbits of 3-d dynamical systems admitting a Poincaré section can

be described as braids. This characterisation can be transported to the

Poincaré section and Poincaré map, resulting in the braid type.

Information from braid types allows to estimate bounds for the topological

entropy of the map while revealing detailed orbit information from the

original system, such as the orbits that are necessarily present along with

the given one(s) and their organisation. We review this characterisation

with some examples --from a user-friendly perspective--,

focusing on systems whose Poincaré section is homotopic to a disc.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Braids - Periodic orbits of 3-d dynamical systems - Poincaré section
in
Topology and Dynamics of Chaos
editor
Letellier, Christophe and Gilmore, Robert
pages
149 - 168
publisher
World Scientific
ISBN
9789814434850 (print)
978-981-4434-87-4
DOI
10.1142/9789814434867_0007
language
English
LU publication?
yes
id
8100cdb7-00ea-48cb-8181-4edce9cb0987 (old id 3412015)
date added to LUP
2013-04-09 11:03:05
date last changed
2016-09-29 10:14:50
@inbook{8100cdb7-00ea-48cb-8181-4edce9cb0987,
  abstract     = {Periodic orbits of 3-d dynamical systems admitting a Poincaré section can <br/><br>
be described as braids. This characterisation can be transported to the <br/><br>
Poincaré section and Poincaré map, resulting in the braid type. <br/><br>
Information from braid types allows to estimate bounds for the topological <br/><br>
entropy of the map while revealing detailed orbit information from the <br/><br>
original system, such as the orbits that are necessarily present along with<br/><br>
the given one(s) and their organisation. We review this characterisation <br/><br>
with some examples --from a user-friendly perspective--, <br/><br>
focusing on systems whose Poincaré section is homotopic to a disc.},
  author       = {Natiello, Mario and Solari, Hernán G},
  editor       = {Letellier, Christophe and Gilmore, Robert},
  isbn         = {9789814434850 (print)},
  keyword      = {Braids - Periodic orbits of 3-d dynamical systems - Poincaré section},
  language     = {eng},
  pages        = {149--168},
  publisher    = {World Scientific},
  series       = {Topology and Dynamics of Chaos},
  title        = {A Braided View of a Knotty Story},
  url          = {http://dx.doi.org/10.1142/9789814434867_0007},
  year         = {2013},
}