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摘要翻译：
我们介绍并研究了Halphen连分式理论的高属推广。我们的基本概念是超椭圆Haplhen(HH)元素$$\frac{\sqrt{X_{2g+2}}-\sqrt{Y_{2g+2}}{x-y}，$$取决于参数$y$，其中$X_{2g+2}$是一个次数$2g+2$的多项式，$Y_{2g+2}=X_{2g+2}(y)$。我们研究了规则和不规则HH元素。它们的连分式展开以及这种展开的一些基本性质：奇偶对称性和周期性。
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英文标题：
《Multi-valued hyperelliptic continued fractions of generalized Halphen
type》
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作者：
Vladimir Dragovic
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We introduce and study higher genera generalizations of the Halphen theory of continued fractions. The basic notion we start with is hyperelliptic Haplhen (HH) element $$\frac{\sqrt{X_{2g+2}}-\sqrt{Y_{2g+2}}}{x-y},$$ depending on parameter $y$, where $X_{2g+2}$ is a polynomial of degree $2g+2$ and $Y_{2g+2}=X_{2g+2}(y)$. We study regular and irregular HH elements. their continued fraction development and some basic properties of such development: even and odd symmetry and periodicity.
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PDF链接：
https://arxiv.org/pdf/0809.4931
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