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.
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 language | English |
|---|---|
| Title of host publication | Topology and Dynamics of Chaos |
| Editors | Christophe Letellier, Robert Gilmore |
| Publisher | World Scientific Publishing |
| Pages | 149-168 |
| ISBN (Print) | 9789814434850 (print), 978-981-4434-87-4 |
| DOIs | |
| Publication status | Published - 2013 |
Subject classification (UKÄ)
- Mathematics
Keywords
- Braids - Periodic orbits of 3-d dynamical systems - Poincaré section