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A 1-Lipschitz map f from a convex compact set to itself has fixed points. This consequence of Brouwer's or Schauder's fixed point theorem has more elementary proofs by approximating f by λ-contractions, fλ. We study the ...
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We derive a discrete version of the results of our previous work. If M is a compact metric space, c:M×M→ℝ a continuous cost function and λ∈(0,1), the unique solution to the discrete λ-discounted equation is the only func...
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The two main results of this paper concern the regularity of the invariant foliation of a C0-integrable symplectic twist diffeomorphisms of the 2-dimensional annulus, namely that • the generating function of such a folia...