- Huyi Hu, Michigan State University
- Quasi-stability for partially hyperbolic diffeomorphisms
- 03/02/2023
- 3:00 PM - 4:00 PM
- A126 Wells Hall
- Huyi Hu (hhu@msu.edu)
The motivation of the work is to study topological properties of
partially hyperbolic systems which are similar to those of uniformly hyperbolic systems. We try to obtain some properties similar to these of uniformly hyperbolic systems by ``ignoring'' the motions along the center direction.
We show that any partially hyperbolic systems are quasi-stable in the sense that for any homeomorphism $g$ $C^0$-close to $f$, there exist a continuous map $\pi$ from $M$ to itself and a family of locally defined continuous maps $\{\tau_x\}$, which send points along the center direction, such that
$$\pi\circ g=\tau_{fx}\circ f\circ\pi.
$$
In particular, if $f$ has $C^1$ center foliation, then we can make the motion $\tau$ along the center foliation.
As application we obtain some continuity properties for topological entropy.
