非自治Conley指标理论：连接同态
Nonautonomous Conley Index Theory: The Connecting Homomorphism
摘要：
孤立不变集的吸引-排斥分解产生所谓的连接同态。这些同态揭示了底层动力系统的连接轨迹的存在和结构的信息。为了给一个有意义的一般原则，非自治问题，非自治的同源康利指数表示为一个直接的限制。此外，它表明，一个非平凡的连接同态意味着，在动力系统水平上，一种一致的吸引子-排斥子分解的连通性。
英文摘要：
Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical system. To give a meaningful generalization of this general principle to nonautonomous problems, the nonautonomous homology Conley index is expressed as a direct limit. Moreover, it is shown that a nontrivial connecting homomorphism implies, on the dynamical systems level, a sort of uniform connectedness of the attractor-repeller decomposition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
