Saturation of Generalized Partially Hyperbolic Attractors
Abstract
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 diffeomorphism has zero volume. In contrast, by modification of Poincar\'e cross section of the geometric model, we build a C1-diffeomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.
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