On Recurrent maps on interval

Abstract

An operator $T$ acting on a metric compact space $X$ is said to be recurrent if for each $U$; a nonempty open subset of $X$, there exists $n\in\mathbb{N}$ such that $T^n(U)\cap U\neq\emptyset$. In this paper, we introduce and study the notion of recurrence of interval map. We investigate some properties of this class of operators and show the links between recurrence, R-mixing and weakly R-mixing of operators and interval maps.