Introduction

Abstract

If f : X → X is a continuous map and x ∈ X, we say that y is a limit point for the associated dynamical system with initial value x, or y is an ω limit point of x, when y is a limit point of the orbit sequence {f ⁿ(x) : n ∈ T} where T is the set of nonnegative integers. This means that the sequence enters every neighborhood of y infinitely often. That is, for any open set U containing y, the entrance time set N(x,U) = {n ∈ T : f ⁿ(x) ∈ U} is infinite.