thisbookprovidesthefirstself-containedcomprehensiveexpositionofthetheoryofdynamicalsystemsasacoremathematicaldisciplinecloselyintertwinedwithmostofthemainareasofmathematics.theauthorsintroduceandrigorouslydevelopthetheorywhileprovidingresearchersinterestedinapplicationswithfundamentaltoolsandparadigms.thebookbeginswithadiscussionofseveralelementarybutfundamentalexamples.theseareusedtoformulateaprogramforthegeneralstudyofasymptoticpropertiesandtointroducetheprincipaltheoreticalconceptsandmethods.themainthemeofthesecondpartofthebookistheinterplaybetweenlocalanalysisnearindividualorbitsandtheglobalcomplexityoftheorbitstructure.thethirdandfourthpartsdevelopindepththetheoriesof！ow-dimensionaldynamicalsystemsandhyperbolicdynamicalsystems.thebookisaimedatstudentsandresearchersinmathematicsatalllevelsfromad-vancedundergraduateup.scientistsandengineersworkinginapplieddynamics，non-linearscience，andchaoswillalsofindmanyfreshinsightsinthisconcreteandclearpresentation.itcontainsmorethanfourhundredsystematicexercises.