Simple dynamical systems


  • Kamaludheen Ali Akbar Central University of Kerala
  • V. Kannan University of Hyderabad
  • I. Subramania Pillai Pondicherry University



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


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 â—¦ f = f â—¦ h and h(x) = y. An element x ∈ R is ordinary in (R,f) if its equivalence class [x] is a neighbourhood of it.


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Author Biographies

Kamaludheen Ali Akbar, Central University of Kerala

Department of Mathematics

V. Kannan, University of Hyderabad

School of Mathematics and Statistics

I. Subramania Pillai, Pondicherry University

Department of Mathematics


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How to Cite

K. Ali Akbar, V. Kannan, and I. Subramania Pillai, “Simple dynamical systems”, Appl. Gen. Topol., vol. 20, no. 2, pp. 307–324, Oct. 2019.