Partially Hyperbolic Dynamics on ${\mathbb{T}}^4$: Existence of Compact Center-Unstable Leaves

Raul Ures, Tongyao Yu

We show that for $n\ge 2$, if a partially hyperbolic diffeomorphism $f:{\mathbb{T}}^{n+1}\to {\mathbb{T}}^{n+1}$ with $\dim E^s=\dim E^c=1$ has an invariant center-unstable foliation with…