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The class of simple dynamics systems. (English) Zbl 1452.37021

Summary: In this paper, we study the class of simple dynamical systems on \(\mathbb{R}\) induced by continuous maps having finitely many non-ordinary points. We characterize this class using labeled digraphs and dynamically independent sets. In fact, we classify dynamical systems up to their number of non-ordinary points. In particular, we discuss about the class of continuous maps having unique non-ordinary point, and the class of continuous maps having exactly two non-ordinary points.

MSC:

37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
26A21 Classification of real functions; Baire classification of sets and functions
26A48 Monotonic functions, generalizations
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References:

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