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

Giesl, Peter (2020) On a matrix-valued PDE characterizing a contraction metric for a periodic orbit. Discrete and Continuous Dynamical Systems - Series B (DCDS-B). pp. 1-27. ISSN 1531-3492

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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 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.

Item Type: Article
Keywords: Periodic orbit, stability, contraction metric, converse theorem, matrix-valued
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 09 Sep 2020 09:34
Last Modified: 27 Oct 2021 01:00
URI: http://sro.sussex.ac.uk/id/eprint/93644

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