Mathematical Sciences: Dynamical Systems and Applications

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The principal investigator will develop and improve methods for understanding bifurcation from invariant tori, semi-linear elliptic problems in unbounded domains, and singularly perturbed differentiable systems. The underlying technique is the theory of invariant manifolds. Dynamical systems encompass both ordinary and partial differential equations, expressing a geometric approach to the study of such equations. An understanding of invariant manifolds is extremely critical as it gives a great deal of information about behavior of solutions in a neighborhood of special solutions.