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Journals and Conferences
5.0. Medical management of active Crohn's disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.
LetM be the four-dimensional compact manifoldM = T 2×S2 and let k ≥ 2. We construct a C∞ diffeomorphism F : M → M with precisely k intermingled minimal attractors A1, . . . , Ak. Moreover the union of the basins is a set of full Lebesgue measure. This means that Lebesgue almost every point in M lies in the basin of attraction of Aj for some j, but every… (More)
We prove the existence of mixed spectrum C∞ reparameterizations of any linear flow on T2 with Liouville rotation number. For a restricted class of Liouville rotation numbers we prove the existence of mixed spectrum real-analytic reparameterizations.
We show that given any tiling of Euclidean space, any geometric patterns of points, we can find a patch of tiles (of arbitrarily large size) so that copies of this patch appear in the tiling nearly centered on a scaled and translated version of the pattern. The rather simple proof uses Furstenberg’s topological multiple recurrence theorem.
We consider the dependence on parameters of the solutions of cohomology equations over Anosov diffeomorphisms. We show that the solutions depend on parameters as smoothly as the data. As a consequence we prove optimal regularity results for the solutions of equations taking value in diffeomorphism groups. These results are motivated by applications to… (More)