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arXiv · 1511.06996

Differential positivity characterizes one-dimensional normally hyperbolic attractors

Fulvio Forni·Alexandre Mauroy·Rodolphe Sepulchre
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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.

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Fulvio Forni, Alexandre Mauroy, Rodolphe Sepulchre. 2015-11-22. Differential positivity characterizes one-dimensional normally hyperbolic attractors. https://arxiv.org/abs/1511.06996

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