论文标题
射影表面的滤波内态性：无限许多密集轨道的存在
Surjective endomorphisms of projective surfaces: the existence of infinitely many dense orbits
论文作者
论文摘要
令$ f \ colon x \ to x $为正常投射表面的过滤性内态。当$ \ operatorName {deg} f \ geq 2 $，应用（迭代）$ f $ - equivariant模型程序（EMMP）时，我们确定$ x $的几何结构。使用此功能，我们将第二作者的结果扩展到奇异表面，以至于$ x $具有$ f $ invariant的非恒定理性功能，或者$ f $具有无限的许多Zariski浓密的远期轨道；该结果也扩展到Adelic拓扑（比Zariski拓扑更好）。
Let $f \colon X \to X$ be a surjective endomorphism of a normal projective surface. When $\operatorname{deg} f \geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$. Using this, we extend the second author's result to singular surfaces to the extent that either $X$ has an $f$-invariant non-constant rational function, or $f$ has infinitely many Zariski-dense forward orbits; this result is also extended to Adelic topology (which is finer than Zariski topology).
