We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case.

中文翻译：

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连接组合动力学和古典动力学：康利指数和莫尔斯分解

我们证明，在简单复形的一个单纯形族上定义的，在福尔曼意义上的每个组合动力学系统，都会在简单复形的几何实现上产生一个多值动力学系统 F。此外，F的选择方式应使组合矢量场的孤立不变集，Conley索引，Morse分解和Conley-Morse图在多值映射情况下引起同构对象。