American Mathematical Society

Natural Sciences and Engineering Research Council Canada

William F. Langford

F. V. Atkinson

Angelo Bernardo Mingarelli

Canadian Mathematical Congress (Society)

Seminar on Oscillation, Bifurcation, and Chaos (1986 : University of Toronto)

The year 1986 marked the sesquicentennial of the publication in 1836 of J. Sturm's classic memoir on boundary value problems for second order equations. In July 1986, the Canadian Mathematical Society sponsored the International Conference on Oscillation, Bifurcation, and Chaos, held at the University of Toronto. This volume contains the proceedings of this conference. Requiring a basic knowledge of the qualitative theory of differential equations, this book is aimed at mathematicians and students working in any area of differential equations, as well as researchers interested in applying recent results in oscillation and bifurcation theory to other disciplines. Readers will gain a broad perspective on current research in this area from both the Sturmian and dynamical systems points of view, as well as an understanding of new results useful for application and of directions for future research.

Proceedings of the 1986 Annual Seminar Held July 13-25, 1986

Oscillation, Bifurcation and Chaos

Wayne Nagata

This volume presents new research on normal forms, symmetry, homoclinic cycles, and chaos, from the Workshop on Normal Forms and Homoclinic Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in November 1992, in Waterloo, Canada. The workshop bridged the local and global analysis of dynamical systems with emphasis on normal forms and the recently discovered homoclinic cycles which may arise in normal forms. Specific topics covered in this volume include normal forms for dissipative, conservative, and reversible vector fields, and for symplectic maps; the effects of symmetry on normal forms; the persistence of homoclinic cycles; symmetry-breaking, both spontaneous and induced; mode interactions; resonances; intermittency; numerical computation of orbits in phase space; applications to flow-induced vibrations and to mechanical and structural systems; general methods for calculation of normal forms; and chaotic dynamics arising from normal forms. Of the 32 presentations given at this workshop, 14 of them are represented by papers in this volume.

Normal Forms and Homoclinic Chaos

William F. Langford

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