Complete description of the Lyapunov spectra of~continuous families of~linear differential systems with

V. V. Bykov

Izvestiya. Mathematics , Tome 84 (2020) no. 6, pp. 1037-1055.

Résumé

For every positive integer $n$ and every metric space $M$ we consider the class $\widetilde{\mathcal{U}}^n(M)$ of all parametric families $\dot x = A(t, \mu)x$, where $x\in\mathbb{R}^n$, $t\geqslant 0$, $\mu\in M$, of linear differential systems whose coefficients are piecewise continuous and, generally speaking, unbounded on the time semi-axis for every fixed value of the parameter $\mu$ such that if a sequence $(\mu_k)$ converges to $\mu_0$ in the space of parameters, then the sequence $(A(\,{\cdot}\,,\mu_k))$\linebreak converges uniformly on the semi-axis to the matrix $A(\,{\cdot}\,,\mu_0)$. For the families in $\widetilde{\mathcal{U}}^n(M)$, we obtain a complete description of individual Lyapunov exponents and their spectra as functions of the parameter.

Détail

Keywords: linear differential system, Lyapunov exponents
Mots-clés : infinitesimal perturbations, Baire classes.

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