Topological Entropy of Braids on the Torus

Details Topological Entropy of Braids on the Torus Topological Entropy of Braids on the Torus

2006-05-11

arxiv.org/abs/nlin/0605026v1

SIAM J. Applied Dyn. Sys. 6, 79-98 (2007)

Nonlinear Sciences

Chaotic Dynamics

19 pages, 44 figures. SIAM journal style

Scientific paper

10.1137/060659636

A fast method is presented for computing the topological entropy of braids on the torus. This work is motivated by the need to analyze large braids when studying two-dimensional flows via the braiding of a large number of particle trajectories. Our approach is a generalization of Moussafir's technique for braids on the sphere. Previous methods for computing topological entropies include the Bestvina--Handel train-track algorithm and matrix representations of the braid group. However, the Bestvina--Handel algorithm quickly becomes computationally intractable for large braid words, and matrix methods give only lower bounds, which are often poor for large braids. Our method is computationally fast and appears to give exponential convergence towards the exact entropy. As an illustration we apply our approach to the braiding of both periodic and aperiodic trajectories in the sine flow. The efficiency of the method allows us to explore how much extra information about flow entropy is encoded in the braid as the number of trajectories becomes large.

Affiliated with

Also associated with

No associations

Rating

Topological Entropy of Braids on the Torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological Entropy of Braids on the Torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological Entropy of Braids on the Torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-469747