Asymptotic of the largest Floquet multiplier for cooperative matrices

Carmona, Philippe

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

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 $\frac{\mathrm{d}x}{\mathrm{d}t}\left(t\right)=A\left(t\right)x\left(t\right)$, avec $A\left(t\right)$ une matrice coopérative irréductible, avec la moyenne de l’abcisse spectrale ${\int }_0^{1}s\left(A\left(u\right)\right)\mathrm{d}u$.

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 $\frac{\mathrm{d}x}{\mathrm{d}t}\left(t\right)=A\left(t\right)x\left(t\right)$, with $A\left(t\right)$ a cooperative irreducible matrix, and the mean spectral abscissa ${\int }_0^{1}s\left(A\left(u\right)\right)\mathrm{d}u$.

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

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