Differential positivity characterizes one-dimensional normally hyperbolic attractors
This provides a theoretical characterization for a class of attractors in dynamical systems, but the result is incremental as it extends an existing framework.
The paper proves that normally hyperbolic one-dimensional compact attractors of smooth dynamical systems are characterized by differential positivity, analogous to how zero-dimensional hyperbolic attractors are characterized by differential stability.
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.