Saturation of Generalized Partially Hyperbolic Attractors
Dynamical Systems
2018-11-29 v4
Abstract
We 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 Poincar\'e cross section of the geometric model, we build a -diffeomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.
Cite
@article{arxiv.1408.1835,
title = {Saturation of Generalized Partially Hyperbolic Attractors},
author = {A. Fakhari and M. Soufi},
journal= {arXiv preprint arXiv:1408.1835},
year = {2018}
}