A Braided View of a Knotty Story
(2013) 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:
https://lup.lub.lu.se/record/3412015
- author
- Natiello, Mario LU and Solari, Hernán G
- organization
- publishing date
- 2013
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Braids - Periodic orbits of 3-d dynamical systems - Poincaré section
- host publication
- Topology and Dynamics of Chaos
- editor
- Letellier, Christophe and Gilmore, Robert
- pages
- 149 - 168
- publisher
- World Scientific Publishing
- 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
- 2016-04-04 12:04:35
- date last changed
- 2021-01-25 10:54:26
@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}}, booktitle = {{Topology and Dynamics of Chaos}}, editor = {{Letellier, Christophe and Gilmore, Robert}}, isbn = {{9789814434850 (print)}}, keywords = {{Braids - Periodic orbits of 3-d dynamical systems - Poincaré section}}, language = {{eng}}, pages = {{149--168}}, publisher = {{World Scientific Publishing}}, title = {{A Braided View of a Knotty Story}}, url = {{http://dx.doi.org/10.1142/9789814434867_0007}}, doi = {{10.1142/9789814434867_0007}}, year = {{2013}}, }