Fiedler, Bernold.
Global Bifurcation of Periodic Solutions with Symmetry [electronic resource] / by Bernold Fiedler. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1988. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1309 0075-8434 ; . - Lecture Notes in Mathematics, 1309 .
Main results -- No symmetry — a survey -- Virtual symmetry -- Generic local theory -- Generic global theory -- General global theory -- Applications -- Discussion -- Appendix on genericity.
This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.
9783540391500
10.1007/BFb0082943 doi
Mathematics.
Global analysis (Mathematics).
Mathematical physics.
Mathematics.
Analysis.
Mathematical and Computational Physics.
QA299.6-433
515
Global Bifurcation of Periodic Solutions with Symmetry [electronic resource] / by Bernold Fiedler. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1988. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1309 0075-8434 ; . - Lecture Notes in Mathematics, 1309 .
Main results -- No symmetry — a survey -- Virtual symmetry -- Generic local theory -- Generic global theory -- General global theory -- Applications -- Discussion -- Appendix on genericity.
This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.
9783540391500
10.1007/BFb0082943 doi
Mathematics.
Global analysis (Mathematics).
Mathematical physics.
Mathematics.
Analysis.
Mathematical and Computational Physics.
QA299.6-433
515