94-278 Ch. Bonatti, L. J. Diaz, M. Viana

Discontinuity of the Hausdorff dimension of hyperbolic sets (14K, AMSTeX) Sep 2, 94

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Abstract. We prove that the Hausdorff dimension of a hyperbolic basic set may vary discontinuously with the dynamics if the dimension of the ambient manifold is bigger than two. This loss of continuity is associated to the occurrence of intersections between the stable (resp. unstable) manifold and the strong unstable (resp. strong stable) manifold of some periodic point.

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