Simple dynamical systems

Abstract

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In this paper, we study the class of simple systems on </span><span>R </span><span>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 </span><span>x,y </span><span>∈ </span><span>R</span><span>, we say </span><span>x </span><span>∼ </span><span>y </span><span>on a dynamical system (</span><span>R</span><span>,f</span><span>) if </span><span>x </span><span>and </span><span>y </span><span>have same dynamical properties, which is an equivalence relation. Said precisely, </span><span>x </span><span>∼ </span><span>y </span><span>if there exists an increasing homeomorphism </span><span>h </span><span>: </span><span>R </span><span>→ </span><span>R </span><span>such that </span><span>h </span><span>◦ </span><span>f </span><span>= </span><span>f </span><span>◦ </span><span>h </span><span>and </span><span>h</span><span>(</span><span>x</span><span>) = </span><span>y</span><span>. </span><span>An element </span><span>x </span><span>∈ </span><span>R </span><span>is </span><span>ordinary </span><span>in (</span><span>R</span><span>,f</span><span>) if its equivalence class [</span><span>x</span><span>] is a neighbourhood of it.</span></p><p><span><br /></span></p></div></div></div>