The Morse equation in the Conley index theory for discrete multivalued dynamical systems

2022/01/31 by Bogdan Batko, Batko, Bogdan
Computer Science · Mathematics · Physics and Astronomy · #37B25 #37B35 #37M10 #54C60 #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #primary 54H20 #secondary 37B30

paper · pdf · doi:10.48550/arxiv.2202.00152

openalex publication_date 2022/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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