Saturation of generalized partially hyperbolic attractors. Issue 3 (3rd July 2019) - Fakhari, Abbas; Soufi, Mohammad
ABSTRACT: We prove the saturation of a generalized partially hyperbolic attractor of a C 2 map. As a consequence, we show that any generalized partially hyperbolic horseshoe-like attractor of a C 1 -generic diffeomorphism has zero volume. In contrast, by modification of the Poincaré cross section of Lorenz geometric model, we build a C 1 -diffeomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.