Simple dynamical systems

Authors

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

DOI:

https://doi.org/10.4995/agt.2019.7910

Keywords:

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

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 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

References

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B. Sankara Rao, I. Subramania Pillai and V. Kannan, The set of dynamically special points, Aequationes Mathematicae 82, no. 1-2 (2011), 81-90. https://doi.org/10.1007/s00010-010-0066-6

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Published

2019-10-01

How to Cite

[1]
K. Ali Akbar, V. Kannan, and I. Subramania Pillai, “Simple dynamical systems”, Appl. Gen. Topol., vol. 20, no. 2, pp. 307–324, Oct. 2019.

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