AI 中文总结
该研究针对合作系统“呈一维特征”、2-合作系统“呈二维特征”的现象，基于正锥上射影度量的Birkhoff-Hilbert压缩，提供几何直观解释，补充相关维数约简的理论依据。
AI 中文摘要
已知合作系统，更一般地说，对锥单调的系统，在适当不可约条件下表现得如同一维系统，这一点可由Hirsch的一般收敛定理等结果佐证。Sanchez等人的研究还表明，2-合作系统（即保持通常非凸二维锥的系统，通过符号变化减少来检验）表现得如同二维系统，这可由类Poincaré-Bendixson定理佐证。本文基于正锥上射影度量的Birkhoff-Hilbert压缩，尝试为这些维数约简提供几何直观解释。
英文摘要
It is known that cooperative systems, and more generally systems monotone with respect to cones, behave under appropriate irreducibility conditions like one-dimensional systems, as evidenced by results such as Hirsch's generic convergence theorem. It is also known, following work of Sanchez and others, that two-cooperative systems, those preserving a generally nonconvex 2-dimensional cone (tested through the diminishing of sign variations), behave like two-dimensional systems, as evidenced by Poincare--Bendixson-type theorems. In these notes I attempt to give some geometric intuition for these dimensionality reductions, based on Birkhoff--Hilbert contractions of the projective metric on a positive cone.
