The Study Of The Set Of Banach Positive Upper Density Recurrent Points In Continuous Dynamical Systems

In this thesis, we mainly study an especial recurrent level in continuousdynamical systems, which is the properties of Banach positive upper density recurrentpoints. Similar to the properties of the set of recurrent points, in this thesis, wemake a systematic study for the properties of Banach positive upper density recurrentpoints. This thesis is divided into four chapters.The first chapter gives a detailed description on the research background.The second chapter introduces some basic concepts and conclusions used in thisthesis.In the third chapter, we study the properties of Banach positive upper densityrecurrent points, and give some equivalent conditions for a point in a continuousdynamical system to be a Banach positive upper density recurrent point. Subsequently,we discuss the relationship between Banach positive upper density recurrent pointsand measure center.In the fourth chapter, by using the properties of Banach positive upper densityrecurrent points, we present some equivalent conditions for a continuous dynamicalsystem to be an E-system.