Endomorphisms of the plane preserving a pencil of curves

环面上保面积部分双曲自同态传递性的一个判据

A criterion for transitivity of area preserving partially hyperbolic endomorphism on torus

本文提出 n 阶横截性判据以判定环面上保面积部分双曲自同态的传递性，并进一步回答何宝林所提出的 Gan 问题。

Rational Endomorphisms of Codimension One Holomorphic Foliations

In this work, we study dominant rational maps preserving singular holomorphic codimension one foliations on projective manifolds and that exhibit non-trivial transverse dynamics.

部分双曲自同态的遍历性

Ergodicity Of Partially Hyperbolic Endomorphisms

本文证明了在保体积、部分双曲、中心丛状且具有常Jacobian的条件下，自同态的本质可达性可推出其遍历性。

Transitivity of conservative toral endomorphisms

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in any smoothness category, of those homotopy classes of conservative endomorphisms that consist entirely of transitive maps.

椭圆曲线Hesse模空间的几何自同态

Geometric Endomorphisms of the Hesse moduli space of elliptic curves

本文研究椭圆曲线Hesse模空间上Cayleyan映射与Hessian映射生成的自由半群，分析其几何与动力学性质，并揭示两者在实周期点数量和Julia集上的显著差异。

Integral points and orbits of endomorphisms on the projective plane

We analyze when integral points on the complement of a finite union of curves in $\mathbb{P}^2$ are potentially dense. We divide the analysis of these affine surfaces based on their logarithmic Kodaira dimension $\barκ$. When $\barκ = -\infty$, we completely characterize the potential density of integral points in terms of the number of irreducible components on the surface at infinity and the number of multiple members in a pencil naturally associated to the surface. When integral points are not potentially dense, we show that they lie on finitely many effectively computable curves. When $\ba…