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This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin...

We all know that determining the homotopy groups of a topological space is one of the central problems in homotopy theory. There is always a deep relation between the homotopy groups and other mathematical invariants which have wide applications in many fields such as geometric topology, algebra, algebraic K-theory and algebraic geometry. Via the view of homotopy theory, we try to approach the homotopy groups from two different sides: (i) Consider the general property of homotopy groups such as homotopy exponent; (ii) Consider the computation of stable homotopy groups of spheres.

This book concerns a central problem in algebraic topology-stable homotopy groups of spheres. Ever since J. P. Serres historic result showed that the homotopy groups of spheres are finitely generated in 1950s, the determination of homotopy groups of spheres has always been the focus of algebraic topologists. Up to now, still much has not been known to us. In our book, we consider the stable part of the homotopy groups of spheres. We will mainly apply two computation tools to detect nontrivial elements of the stable homotopy groups of spheres-Adams spectral sequence and May spectral sequence....