English

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 C2C^2 map. As a consequence, we show that any generalized partially hyperbolic horseshoe-like attractor of a C1C^1-generic diffeomorphism has zero volume. In contrast, by modification of Poincar\'e cross section of the geometric model, we build a C1C^1-diffeomorphism with a partially hyperbolic horseshoe-like attractor of positive volume.

Keywords

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}
}
R2 v1 2026-06-22T05:23:09.488Z