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Global Bifurcation of Periodic Solutions with Symmetry (Paperback, 1988 ed.)
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Global Bifurcation of Periodic Solutions with Symmetry (Paperback, 1988 ed.)
Series: Lecture Notes in Mathematics, 1309
Expected to ship within 10 - 15 working days
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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.
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