论文标题
部分可观测时空混沌系统的无模型预测
Hyperbolic manifolds with a large number of systoles
论文作者
论文摘要
在本文中，对于任何$ n \ geq 4 $，我们构造了一系列紧凑的双曲线$ n $ -n $ -manifolds $ \ {m_i \} $，其系统数至少为$ \ mathrm {vol}（vol}（m_i）（m_i）^{1+ \ frac {1+\ frac {1}} {3n（n+1）{3n+1} {$ 1）在维度3中，将界限提高到$ \ mathrm {vol}（m_i）^{\ frac {4} {3} {3}-ε} $。这些结果将Schmutz的先前工作以$ n = 2 $概括，而Dória-Murillo则以$ n = 3 $的价格概括为更高的尺寸。
In this article, for any $n\geq 4$ we construct a sequence of compact hyperbolic $n$-manifolds $\{M_i\}$ with number of systoles at least as $\mathrm{vol}(M_i)^{1+\frac{1}{3n(n+1)}-ε}$ for any $ε>0$. In dimension 3, the bound is improved to $\mathrm{vol}(M_i)^{\frac{4}{3}-ε}$. These results generalize previous work of Schmutz for $n=2$, and Dória-Murillo for $n=3$ to higher dimensions.
