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

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  • 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 enables the explicit construction of a contraction metric by numerically solving this equation in [7]. In this paper we prove existence and uniqueness of the solution of the PDE and show that it defines a contraction metric.

    Mathematics Subject Classification: Primary: 34C25, 34D20; Secondary: 37C27.

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