Simple dynamical systems

K. Ali Akbar, V. Kannan, I. Subramania Pillai

Abstract

In this paper, we study the class of simple systems on R induced by homeomorphisms having finitely many non-ordinary points. We characterize the family of homeomorphisms on R having finitely many non-ordinary points upto (order) conjugacy. For x,y ∈ R, we say x ∼ y on a dynamical system (R,f) if x and y have same dynamical properties, which is an equivalence relation. Said precisely, x ∼ y if there exists an increasing homeomorphism h : R → R such that h ◦ f = f ◦ h and h(x) = y. An element x ∈ R is ordinary in (R,f) if its equivalence class [x] is a neighbourhood of it.



Keywords

special points; non-ordinary points; critical points; order conjugacy

Subject classification

54H20; 26A21; 26A48.

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References

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1. Which orbit types force only finitely many orbit types?
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Journal of Difference Equations and Applications  vol: 26  issue: 5  first page: 676  year: 2020  
doi: 10.1080/10236198.2020.1784152



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Universitat Politècnica de València

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