Saturation of generalized partially hyperbolic attractors. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Fakhari, Abbas; Soufi, Mohammad
• Is Part Of: Dynamical systems. Volume 34:Issue 3(2019)
• Page Start: 443
• Page End: 455
• Publication Date: 2019-07-03
• Subjects: Generalized partially hyperbolic attractor -- C1-generic -- horseshoe-like -- Lorenz attractor; 37DXX -- 37XX; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2018.1554029
• Languages: English
• ISSNs: 1468-9367

Abstract

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.