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A geometric approach to invariant sets for dynamical systems

Keywords: Invariant sets , dynamical systems , area functional , steepest descent method

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Abstract:

In this article, we present a geometric framework to study invariant sets of dynamical systems associated with differential equations. This framework is based on properties of invariant sets for an area functional. We obtain existence results for heteroclinic and periodic orbits. We also implement this approach numerically by means of the steepest descent method.

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