Differential positivity characterizes one-dimensional normally hyperbolic attractors
Systems and Control
2015-11-24 v1 Dynamical Systems
Abstract
The paper shows that normally hyperbolic one-dimensional compact attractors of smooth dynamical systems are characterized by differential positivity, that is, the pointwise infinitesimal contraction of a smooth cone field. The result is analog to the characterization of zero-dimensional hyperbolic attractors by differential stability, which is the pointwise infinitesimal contraction of a Riemannian metric.
Cite
@article{arxiv.1511.06996,
title = {Differential positivity characterizes one-dimensional normally hyperbolic attractors},
author = {Fulvio Forni and Alexandre Mauroy and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1511.06996},
year = {2015}
}