Lyapunov exponenets of families of morphisms of generalized Millionshchikov bundles as functions on the base of the bundle

M. V. Karpuk

Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 55-71

Résumé

Parametrized families of linear differential systems with continuous dependence of the solution on the parameter, whose parameter belong to the metric space and coefficients are not necessarily limited on the time half-line are considered. For such families a complete description of Lyapunov exponents as functions of parameter is obtained. In the case when the parameter space is a complete metric space a full description of sets of points of the lower semicontinuity and sets of points of upper semicontinuity of the Lyapunov exponents of such families is obtained. Results are obtained in the general case of the Lyapunov exponents of the families of morphisms of generalized Millionshtchikov bundles.