Let x′ = H(t)x be a non-autonomous Hamiltonian linear differential system. We show that if the rotation number α(λ) for the associated family of systems x′ = (H(t) + λJγ(t))x (where J = (0In-In0) and γ(t) = γ*(t) ≥ 0 for all t) is constant on an interval containing λ = 0, then x′ = H(t)x has an exponential dichotomy.
Exponential dichotomy and rotation number for linear Hamiltonian systems / R. Johnson; M. Nerurkar. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 108:(1994), pp. 201-216. [10.1006/jdeq.1994.1033]
Exponential dichotomy and rotation number for linear Hamiltonian systems
JOHNSON, RUSSELL ALLAN;
1994
Abstract
Let x′ = H(t)x be a non-autonomous Hamiltonian linear differential system. We show that if the rotation number α(λ) for the associated family of systems x′ = (H(t) + λJγ(t))x (where J = (0In-In0) and γ(t) = γ*(t) ≥ 0 for all t) is constant on an interval containing λ = 0, then x′ = H(t)x has an exponential dichotomy.
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