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Lyapunov functions and attractors in arbitrary metric spaces
We prove two theorems concerning Lyapunov functions on metric spaces. The new element in these theorems is the lack of a hypothesis of compactness or local compactness. The first theorem applies to a discrete dynamical system on any metric space; the result is that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper …