On the Perturbations of the Lyapunov Exponents of Discrete Linear System

In case of sequence of matrices we define the characteristic exponent ( ) ( ) N n n ∈ Δ = Δ ( ) Δ λ as a exponent of ( ) ( ) N n n ∈ Δ . It is well known [2] that the set of all Lyapunov exponents of system (1) contains at most s elements, say ) ( ... ) ( ) ( 2 1 A A A r λ λ λ < < < and the set { } ) ( ),..., ( 1 A A r λ λ is called the spectrum of (1). The greatest and the smallest exponent of (1) we will denote ) A ( g λ and ) (A g λ , respectively. Together with (1) we consider the following disturbed system