Converse theorem on a global contraction metric for a periodic orbit

Giesl, Peter (2019) Converse theorem on a global contraction metric for a periodic orbit. Discrete and Continuous Dynamical Systems - Series A, 39 (9). pp. 5339-5363. ISSN 1078-0947

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Abstract

Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions in all directions perpendicular to the flow are contracted, then there exists a unique periodic orbit, which is exponentially stable and we obtain an upper bound on the rate of exponential attraction. In this paper we study the converse question and show that, given an exponentially stable periodic orbit, a contraction metric exists on its basin of attraction and we can recover the upper bound on the rate of exponential attraction.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 20 Mar 2019 08:44
Last Modified: 01 Jul 2019 14:45
URI: http://sro.sussex.ac.uk/id/eprint/82638

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