Abstract
ABSTRACTWe prove the saturation of a generalized partially hyperbolic attractor of a map. As a consequence, we show that any generalized partially hyperbolic horseshoe-like attractor of a -generic diffeomorphism has zero volume. In contrast, by modification of the Poincaré cross section of Lorenz geometric model, we build a -diffeomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.
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