This volume contains the invited papers presented at the 9th International C- ference ¿Dynamical Systems ¿ Theory and Applications¿ held in ?od ¿ z, ¿ Poland, December 17¿20, 2007 dealing with nonlinear dynamical systems. The conf- encegatheredanumerousgroupofscientistsandengineers,whodealwithwidely understoodproblemsofdynamicsmetalsoinengineeringanddailylife. Organizationof the conferencewould nothavebeen possiblewithouta great effortofthestaffoftheDepartmentofAutomaticsandBiomechanicsoftheTech- calUniversityof?od ¿ z. ¿ Thepatronageovertheconferencehasbeentakenbythef- lowingscienti?cinstitutions: MechanicsandMachineDynamicsCommitteesofthe PolishAcademyofSciences, PolishSocietyofTheoreticalandAppliedMech- ics, PolishAssociationforComputationalMechanics,andTechnicalCommitteeof NonlinearOscillationsofIFToMM. The ?nancial support has been given by the Department of Education at the ?¿odz¿ City Hall, Ministry of National Education and the Polish Association for ComputationalMechanics. We welcomednearly100personsfrom13countriesallovertheworld. They decidedto share the results of their researchandmanyyears of experiencein a disciplineofdynamicalsystemsbysubmittingmanyinterestingpapers. TheScienti?cCommitteeincludesthefollowingmembers: IgorV.Andrianov¿ Aachen;JanAwrejcewicz ¿?od ¿ z; ¿ Jose M.