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arXiv · 1408.1835

Saturation of Generalized Partially Hyperbolic Attractors

A. Fakhari·M. Soufi
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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 Poincar\'e cross section of the geometric model, we build a $C^1$-diffeomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.

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A. Fakhari, M. Soufi. 2014-08-08. Saturation of Generalized Partially Hyperbolic Attractors. https://arxiv.org/abs/1408.1835

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