SYSYDSNov 22, 2015

Differential positivity characterizes one-dimensional normally hyperbolic attractors

arXiv:1511.069962 citationsh-index: 57
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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.

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