Many applications involve dynamical systems in non-locally compact infinite dimensional spaces; for example, dynamical systems generated by partial differential equations and delay differential or functional differential equations. Because of the complexities involved in doing detailed analysis in infinite dimensions, these systems often are approximated by finite dimensional dynamical systems generated by ordinary differential equations in ℝn or on a n-dimensional manifold M. The global theory of such dynamical systems is then used to better understand the complete dynamics of the system and the way that the system behaves as physical parameters are varied.
KeywordsFunctional Differential Equation Global Theory Infinite Dimension Parabolic Partial Differential Equation Infinite Dimensional System
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