Remarks on Braid Theory and the characterisation of periodic orbits

Abstract:
The relationship between Braid Theory and the organisation of periodic orbits of dynamical systems is considered.



It is shown that for some (physically relevant) 3-d flows the characterisation of periodic orbits by means of Braid Theory can be done on the Poincaré surface in an efficient way. The result is a thread-less graphical presentation of a braid class.



We discuss extensions of this approach to (adequate) dynamical systems of dimension higher than three, using results from Central Manifold Theory.