On a matrix-valued PDE characterizing a contraction metric for a periodic orbit

Peter Giesl

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arXiv · 1808.02691

On a matrix-valued PDE characterizing a contraction metric for a periodic orbit

Peter Giesl

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Abstract

The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the position of the periodic orbit and is robust to perturbations. In this paper we characterize such a Riemannian contraction metric as matrix-valued solution of a linear first-order Partial Differential Equation. This will enable the explicit construction of a contraction metric by numerically solving this equation in future work. In this paper we prove existence and uniqueness of the solution of the PDE and show that it defines a contraction metric.

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Peter Giesl. 2018-08-08. On a matrix-valued PDE characterizing a contraction metric for a periodic orbit. https://arxiv.org/abs/1808.02691

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