Recurrence in Topological Dynamics pp 1-10 | Cite as

# Introduction

Chapter

## 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.

## Keywords

Limit Point Compact Space Uniform Space Semi Group Minimal Subset
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1997