Ledrappier-Young entropy formula for $C^1$ diffeomorphisms with dominated splitting Part 1: Unstable entropy formula and invariance principle

Shaobo Gan, Yao Tong, Jiagang Yang

We study the unstable entropy of $C^1$ diffeomorphisms with dominated splittings. Our main result shows that when the zero Lyapunov exponent has multiplicity one, the center direct…