Prevalence And Generic Convergence For Essentially Strongly Order Preserving Semiflows

In this paper, we mainly study several properties in ordered separable Banachspace, concerning on essentially strongly order-preserving semiflows (essentially SOPsemiflows for short). First of all, we make use of the definition of essentially SOPsemiflows and prevalence to research the prevalence of (quasi-) convergence set. Then,we apply the limit set dichotomy and sequential limit set trichotomy of essentially SOPsemiflows to get the generic convergence of convergence set.This paper is composed of three chapters.In the first chapter, we simply introduce the background, significance and currentsituation of dynamical systems. Not only that we also present a serious of lemmas,definition and symbols what we shall use.In the second chapter, we introduce a more stronger relation, the related propertiesof prevalence and basis knowledge of essentially SOP semiflows, and make use of thenonordering and dichotomy of limit sets to obtain the prevalence of (quasi-) convergenceset.In the third chapter, combining with the basis theorems and properties of essen-tially SOP semiflows which we get the sufcient condition that make the dichotomyof limit sets holding. So we are able to put this conclusion to be extended to moregeneral space. Finaly, we get the generic convergence by the definition of omega limitsets, complements and completes the related result of previous documents.