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The Morse equation in the Conley index theory for discrete multivalued dynamical systems (2202.00152v2)
Published 31 Jan 2022 in math.DS, math.AT, and math.GN
Abstract: A recent generalization of the Conley index to discrete multivalued dynamical systems without a continuous selector is motivated by applications to data-driven dynamics. In the present paper we continue the program by studying attractor-repeller pairs and Morse decompositions in this setting. In particular, we prove Morse equation and Morse inequalities.