C. H. Amon, A. M. Guzmán, and B. Morel, Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging-diverging channel flows, Physics of Fluids, vol.8, pp.1192-1206, 1996.

G. Haller, Lagrangian coherent structures, Annual Review of Fluid Mechanics, vol.47, 2015.

M. R. Allshouse and T. Peacock, Lagrangian-based methods for coherent structure detection, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.25, p.97617, 2015.

J. Weiss, The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D, vol.48, pp.273-294, 1991.

H. Yang, Chaotic transport and mixing by ocean gyre circulation, Stochastic Modelling in Physical Oceanography, pp.439-466, 1996.

G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D: Nonlinear Phenomena, vol.147, 2000.

G. Haller, Lagrangian coherent structures from approximate velocity data, Physics of Fluids, vol.14, pp.1851-1861, 2002.

S. C. Shadden, F. Lekien, and J. E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional, Physica D, vol.212, pp.271-304, 2005.

G. A. Voth, G. Haller, and J. P. Gollub, Experimental measurements of stretching fields in fluid mixing, Phys. Rev. Lett, vol.88, p.254501, 2002.

M. Mathur, G. Haller, T. Peacock, J. E. Ruppert-felsot, and H. L. Swinney, Uncovering the Lagrangian skeleton of turbulence, Phys. Rev. Lett, vol.98, p.144502, 2007.

J. Kasten, C. Petz, I. Hotz, H. Hege, B. R. Noack et al., Lagrangian feature extraction of the cylinder wake, Physics of Fluids, vol.22, p.91108, 2010.

F. Lekien and S. D. Ross, The computation of finite-time Lyapunov exponents on unstructured meshes and for non-euclidean manifolds, Chaos, vol.20, p.17505, 2010.

G. Haller, A variational theory of hyperbolic Lagrangian coherent structures, Physica D, vol.240, pp.574-598, 2011.

M. Farazmand and G. Haller, Computing Lagrangian coherent structures from their variational theory, Chaos, vol.22, p.13128, 2012.

G. Haller and F. J. Beron-vera, Geodesic theory of transport barriers in two-dimensional flows, Physica D: Nonlinear Phenomena, vol.241, pp.1680-1702, 2012.

M. Budi?i? and I. Mezi?, Geometry of the ergodic quotient reveals coherent structures in flows, Physica D: Nonlinear Phenomena, vol.241, pp.1255-1269, 2012.

I. Mezi?, Analysis of fluid flows via spectral properties of the Koopman operator, Annual Review of Fluid Mechanics, vol.45, pp.357-378, 2013.

G. Froyland and K. Padberg-gehle, Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion, Ergodic Theory, Open Dynamics, and Coherent Structures, pp.171-216, 2014.

J. Thiffeault, Braids of entangled particle trajectories, Chaos, vol.20, p.17516, 2010.

A. Borel, Jean leray and algebraic topology, Selected Papers -Oeuvres Scientifiques, vol.1, 1998.

V. I. Arnold, Sur la géométrie differérentielle des groupes de lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier, vol.16, pp.319-361, 1966.

J. Thiffeault, Measuring topological chaos, Phys. Rev. Lett, vol.94, p.84502, 2005.

E. Artin, Theory of braids, Ann. of Math, vol.48, pp.101-126, 1947.

M. R. Allshouse and J. Thiffeault, Detecting coherent structures using braids, Physica D: Nonlinear Phenomena, vol.241, pp.95-105, 2012.

J. Thiffeault and M. Budi?i?, BRAIDLAB: a software package for braids and loops, 2015.

M. Budi?i? and J. Thiffeault, Finite-time braiding exponents, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.25, p.87407, 2015.

N. Francois, H. Xia, H. Punzmann, B. Faber, and M. Shats, Braid entropy of two-dimensional turbulence, Sci. Rep, vol.5, p.18564, 2015.

H. Aref, Stirring by chaotic advection, J. Fluid Mech, vol.143, pp.1-21, 1984.

P. Boyland, Topological methods in surface dynamics, Topology Appl, vol.58, pp.223-298, 1994.

B. Farb and D. Margalit, A Primer on Mapping Class Groups, vol.49, 2012.

D. Bernardete, M. Gutierrez, and Z. Nitecki, A combinatorial approach to reducibility of mapping classes, Mapping Class Groups and Moduli Spaces of Riemann Surfaces, vol.150, pp.1-31, 1993.

D. Bernardete, Z. Nitecki, and M. Gutierrez, Braids and the nielsen-thurston classification, J. Knot Theory Ramifications, vol.4, 1995.

J. S. Birman and T. E. Brendle, Braids: A survey, Handbook of Knot Theory, 2005.

W. Burau, Über zopfgruppen und gleichsinnig verdrillte verkettungen, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol.11, pp.179-186, 1935.

D. Long and M. Paton, The Burau representation is not faithful for n ? 6, Topology, vol.32, pp.439-447, 1993.

S. Bigelow, The Burau representation is not faithful for n = 5, Geometry & Topology, vol.3, pp.397-404, 1999.

T. Church and B. Farb, Infinite generation of the kernels of the Magnus and Burau representations, Algebraic & Geometric Topology, vol.10, pp.837-851, 2010.

G. Band and P. Boyland, The Burau estimate for the entropy of a braid, Algebraic & Geometric Topology, vol.7, pp.1345-1378, 2007.

C. C. Squier, The Burau representation is unitary, Proc. Amer. Math. Soc, vol.90, pp.199-202, 1984.

J. González-meneses, The nth root of a braid is unique up to conjugacy, Algebraic & Geometric Topology, vol.3, pp.1103-1118, 2003.

M. Gates, A. Haidar, and J. Dongarra, Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem, High Performance Computing for Computational Science, pp.182-191, 2015.

J. Kestyn, E. Polizzi, and P. Tang, FEAST eigensolver for non-Hermitian problems, 2015.

J. Boissonnat and M. Yvinec, Algorithmic geometry, 1998.

J. Ottino, The kinematics of mixing: stretching, chaos, and transport, 1989.

M. F. Doherty and J. M. Ottino, Chaos in deterministic systems: strange attractors, turbulence, and applications in chemical engineering, Chemical Engineering Science, vol.43, pp.139-183, 1988.

S. Bigelow, The Lawrence-Krammer representation, Topology and geometry of manifolds (Proc. Sympos. Pure Math.), vol.71, 2003.

T. C. Hu and M. T. Shing, Computation of matrix chain products. part I, SIAM Journal on Computing, vol.11, pp.362-373, 1982.

T. C. Hu and M. T. Shing, Computation of matrix chain products. part II, SIAM J. Comput, vol.13, pp.228-251, 1984.