Leray functor and cohomological Conley index for discrete dynamical systems
Leray functor and cohomological Conley index for discrete dynamical systems
复制标题
离散动力系统的 Leray 函子和上同调康利指数
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
M. Mrozek
中科院分区：
文献类型：
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作者：
M. Mrozek
我们在配备零度自同态的分级模范畴上引入 Leray 函子，并使用该函子定义局部紧度量空间上同胚的孤立不变集的上同调康利指数。我们证明了该指数的同伦性和可加性，并在一些例子中计算了该指数。作为应用之一，我们证明了某个常微分方程组的欧拉近似的非常量有界解的存在性。
We introduce the Leray functor on the category of graded modules equipped with an endomorphism of degree zero and we use this functor to define the cohomological Conley index of an isolated invariant set of a homeomorphism on a locally compact metric space. We prove the homotopy and additivity properties for this index and compute the index in some examples. As one of applications we prove the existence of nonconstant, bounded solutions of the Euler approximation of a certain system of ordinary differential equations.