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Differential positivity characterizes one-dimensional normally hyperbolic attractors (1511.06996v1)
Published 22 Nov 2015 in cs.SY and math.DS
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.