The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
Sheldon E. Newhouse (1979)
Publications Mathématiques de l'IHÉS
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The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
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We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index for vector fields with isolated zeroes in a -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.
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Shadowing lemma for family of -trajectories
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On maximal transitive sets of generic diffeomorphisms
Christian Bonatti, Lorenzo J. Díaz (2003)
Publications Mathématiques de l'IHÉS
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