## Dynamical Systems

•  Yun Yang, Virginia Tech
•  Entropy rigidity for 3D Anosov flows
•  07/25/2022
•  2:00 PM - 3:00 PM
•  C304 Wells Hall
•  Huyi Hu (hhu@msu.edu)

Anosov systems are among the most well-understood dynamical systems. Special among them are the {\bf algebraic systems}. In the diffeomorphism case, these are automorphisms of tori and nilmanifolds. In the flow case, the algebraic models are suspensions of such diffeomorphisms and geodesic flows on negatively curved rank one symmetric spaces. In this talk, we will show that given an integer $k \ge 5$, and a $C^k$ Anosov flow $\Phi$ on some compact connected $3$-manifold preserving a smooth volume, the measure of maximal entropy is the volume measure if and only if $\Phi$ is $C^{k-\varepsilon}$-conjugate to an algebraic flow for $\varepsilon > 0$ arbitrarily small. This is a joint work with Jacopo De Simoi, Martin Leguil and Kurt Vinhage.

## Contact

Department of Mathematics
Michigan State University