A Braided View of a Knotty Story
Author
Editor
- Christophe Letellier
- Robert Gilmore
Summary, in English
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.
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.
Department/s
- Mathematics (Faculty of Engineering)
- Dynamical systems
Publishing year
2013
Language
English
Pages
149-168
Publication/Series
Topology and Dynamics of Chaos
Document type
Book chapter
Publisher
World Scientific Publishing
Topic
- Mathematics
Keywords
- Braids - Periodic orbits of 3-d dynamical systems - Poincaré section
Status
Published
Research group
- Analysis and Dynamics
- Dynamical systems
ISBN/ISSN/Other
- ISBN: 9789814434850 (print)
- ISBN: 978-981-4434-87-4