arXiv subjects

Daohua Yu

Publications and source records attributed to Daohua Yu.

3 recordsLinked to original sources

arXiv2024

Derived from expanding endomorphism on $\mathbb{T}^2$

Assume that $f$ is a $C^r(r\geq 3)$ specially partially hyperbolic endomorphism on the 2-torus which is homotopic to an expanding linear endomorphism $A$ with irrational eigenvalues. We prove that $f$ and $A$ are topologically conjugate, if and only if $f$ is area-expanding. If $f$ is area-expanding and the center bundle is $C^1$, then the topological conjugacy between $f$ and $A$ is $C^{\max\{r-3,1\}+\alpha}$. In particular, if $r=\omega$, the conjugacy is $C^{\omega}$.

math.DS↗

arXiv2024

Uniformly distributed periodic orbits of endomorphisms on $n$-tori

We prove that any ergodic endomorphism on torus admits a sequence of periodic orbits uniformly distributed in the metric sense. As a corollary, an endomorphism on torus is ergodic if and only if the Haar measure can be approximated by periodic measures.

math.DS↗

arXiv2022

Rigidity of center Lyapunov exponents for Anosov diffeomorphisms on 3-torus

Let f and g be two Anosov diffeomorphisms on T3 with three-subbundles partially hyperbolic splittings where the weak stable subbundles are considered as center subbundles. Assume that f is conjugate to g and the conjugacy preserves the strong stable foliation, then their center Lyapunov exponents of corresponding periodic points coincide. This is the converse of the main result of Gogolev and Guysinsky in [9]. Moreover, we get the same result for partially hyperbolic diffeomorphisms derived from Anosov on T3.

math.DS↗