Simple dynamical systems

Kamaludheen Ali Akbar; V. Kannan; I. Subramania Pillai

doi:10.4995/agt.2019.7910

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 âˆˆ R, we say x âˆ¼ y on a dynamical system (R,f) if x and y have same dynamical properties, which is an equivalence relation. Said precisely, x âˆ¼ y if there exists an increasing homeomorphism h : R â†’ R such that h â—¦ f = f â—¦ h and h(x) = y. An element x âˆˆ 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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