Quanta Magazine has recently published a detailed article concerning the research breakthroughs by Thomas Barthelmé (鶹), Kathryn Mann (Cornell University), and Steven Frankel (Washington University in St. Louis). Their work is at the intersection of the theory of dynamical systems, geometry, and topology.
Quanta is a prestigious online publication reporting on the developments in mathematics, theoretical physics, theoretical computer science, and basic life sciences.
The article “Flow Proof Helps Mathematicians Find Stability in Chaos” recounts how chaotic flows have captivated the interest of mathematicians like Henry Poincaré, Jacques Hadamard, Dmitri Anosov, and many others. A classification of an important class of flows, known as Anosov flows, in terms of their periodic trajectories in dimension 3 was achieved by Barthelmé, Frankel and Mann. This is very remarkable since the typical trajectories of such flows are very chaotic and not periodic; therefore the fact that intrinsic information about the global flow can be captured by `exceptional’ trajectories is surprising.