A Braided View of a Knotty Story

Mario Natiello, Hernán G Solari

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

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.
Original languageEnglish
Title of host publicationTopology and Dynamics of Chaos
EditorsChristophe Letellier, Robert Gilmore
PublisherWorld Scientific Publishing
Pages149-168
ISBN (Print)9789814434850 (print), 978-981-4434-87-4
DOIs
Publication statusPublished - 2013

Subject classification (UKÄ)

  • Mathematics

Free keywords

  • Braids - Periodic orbits of 3-d dynamical systems - Poincaré section

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