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Paper   IPM / M / 15538
School of Mathematics
  Title:   Saturation of generalized partially hyperbolic attractors
  Author(s):  Abbas Fakhari (Joint with M. Soufi)
  Status:   To Appear
  Journal: Dynamical Systems: An International Journal
  Supported by:  IPM
We prove the saturation of a generalized partially hyperbolic attractor of a C2 map. As a consequence, we show that any generalized partially hyperbolic horseshoe-like attractor of a C1-generic di eomorphism has zero volume. In contrast, by modi cation of the Poincare cross section of Lorenz geometric model, we build a C1-di eomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.

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