Software

A Matlab toolbox for working with braid groups of punctured disks. Braidlab was initiated by Jean-Luc Thiffeault, and is the most mature piece of software I work on. In addition to algebraic manipulations of braids, braidlab can create braids from space-time curves, e.g., trajectories of dynamical systems, compute their entropies, Thurston-Nielsen type, etc.

A Matlab toolbox implementing the algorithm for computing averages of observables along trajectories of a dynamical system, its ergodic quotient, and finding intrinsic coordinates on the EQ using a machine learning algorithm Diffusion Maps. More on the technique can be found in [https:mbudisic.wordpress.com20140710ergodic-quotient-in-a-finite-time-expanding-context/ this blog entry.

A Matlab toolbox implementing several algorithms for computing the Koopman mode decomposition of dynamical evolution of observables. At this point, the code implements three Dynamic Mode Decomposition variants (with optional debiasing), and a FFT-based algorithm. On top of it, the code finds L2-optimal amplitudes, and plots the spectrum in a compact fashion. The toolbox is not meant to be particularly efficient, but rather of demonstrational character.

Mesochronic analysis uses short-term averages of an incompressible velocity field to find a roadmap for material transport. This Matlab toolbox was used to produce images in the upcoming paper on extensions of 2d mesochronic analysis to 3d incompressible flows.