This principally self-contained learn monograph addresses the next kind of questions. feel one encounters a continual time dynamical process with a few integrated symmetry. may still one count on periodic motions which by some means replicate this symmetry? and the way might periodicity harmonize with symmetry? Probing into those questions leads from dynamics to topology, algebra, singularity idea, and to many purposes. inside a world procedure, the emphasis is on periodic motions faraway from equilibrium. Mathematical tools contain bifurcation concept, transversality conception, and standard approximations. a brand new homotopy invariant is designed to check the worldwide interdependence of symmetric periodic motions. along with mathematical strategies, the ebook includes five mostly nontechnical chapters. the 1st 3 define the most questions, effects and strategies. an in depth dialogue pursues theoretical effects and open difficulties. effects are illustrated via numerous purposes together with coupled oscillators and rotating waves: those hyperlinks to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering opposite numbers make the publication at once available to a much broader viewers.
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