Tag Archives: summary

FTBE paper published in Chaos and braidlab v.3.2 released

I’m happy to report that AIP Chaos published our paper on Finite-Time Braiding Exponents (co-authored with Jean-Luc Thiffeault):
MB. and Thiffeault, J.-L. Finite-time braiding exponents. Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 087407 (2015).

In this paper, we use braid group generators to represent the entangling of trajectories of a dynamical system, and compute the Finite-Time Braiding Exponent (FTBE). FTBE should represent a finite-time, finite-information version of the topological entropy of the flow, and we show evidence that this is really the case.

A graph from the AIP Chaos paper on FTBE.

Mean FTBE and top. entropy correlate, and almost-match as number of strands is increased (Fig. 10 from the paper)

In addition to publishing a paper, we have also released the new version of our MATLAB toolbox braidlab (v.3.2) which was used for all computations in the paper. You can see the release notes on our GitHub repository, as well as download source and compiled versions of the toolbox. Please let us know if you’re using braidlab and, especially, submit any problems with it to our issues page.

Finite-Time Braiding Exponents

Jean-Luc Thiffeault and I have just uploaded our paper on Finite-Time Braiding Exponents (FTBE) to arXiv. In the paper we study how closely topological entropy of a mixing dynamical system can be approximated by sampling only finitely many trajectories from the flow.

Based on numerical results (obtained using braidlab 3.1), we find that FTBEs of finitely-many trajectories converge to topological entropy as number of trajectories is increased. The paper further explores robustness and dependence of  FTBEs on time step, number of trajectories, and their length.