Measuring topological chaos.

@article{Thiffeault2005MeasuringTC,
  title={Measuring topological chaos.},
  author={Jean-Luc Thiffeault},
  journal={Physical review letters},
  year={2005},
  volume={94 8},
  pages={084502}
}
The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A "braiding exponent" is then defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow… CONTINUE READING