Dynamical Systems: Discrete, Continuous and Hybrid

Publication date: 7 July 2023

Abstract: The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation extension) as well as hybrid dynamical systems which combine both continuous time and discrete time dynamics. In a unified way we describe the attractor-repeller structure, Conley's chain recurrence relation and the construction of Lyapunov functions for all of these systems.

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

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