Asymptotic of the largest Floquet multiplier for cooperative matrices

Philippe Carmona

doi:10.5802/afst.1716

Philippe Carmona ¹

¹ Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 4, pp. 1213-1221.

Abstract
Abstract

The aim of this note is to give a link between the spectral radius of the monodromy matrix of a linear differential equation with periodic coefficients $\frac{d x}{d t} (t) = A (t) x (t)$ , with $A (t)$ a cooperative irreducible matrix, and the mean spectral abscissa $\int_{0}^{1} s (A (u)) d u$ .

Le but de cet article est d’établir un lien entre le rayon spectral de la matrice de monodromie d’une équation différentielle linéaire à coefficients périodiques $\frac{d x}{d t} (t) = A (t) x (t)$ , avec $A (t)$ une matrice coopérative irréductible, avec la moyenne de l’abcisse spectrale $\int_{0}^{1} s (A (u)) d u$ .

Received: 2020-05-14
Accepted: 2020-08-25
Published online: 2022-10-28

DOI: 10.5802/afst.1716

Classification: 15A18, 34D08, 15A42, 15B46, 60J80
Keywords: Floquet’s theorem, spectral radius, spectral abscissa, ordinary differential equation, non negative matrices
Mot clés : théorème de Floquet, rayon spectral, abscisse spectrale, équation différentielle ordinaire, matrices à coefficients positifs

Author's affiliations:

Philippe Carmona ¹

¹ Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Asymptotic of the largest {Floquet} multiplier for cooperative matrices},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1213--1221},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Philippe Carmona. Asymptotic of the largest Floquet multiplier for cooperative matrices. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 4, pp. 1213-1221. doi : 10.5802/afst.1716. https://afst.centre-mersenne.org/articles/10.5802/afst.1716/

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