Exponential dichotomy and rotation number for linear hamiltonian systems

Russell Johnson, Mahesh Nerurkar

Research output: Contribution to journalArticle

25 Citations (Scopus)

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 = (0 In -In 0) 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.

Original languageEnglish (US)
Pages (from-to)201-216
Number of pages16
JournalJournal of Differential Equations
Volume108
Issue number1
DOIs
StatePublished - Jan 1 1994

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Hamiltonians
Exponential Dichotomy
Rotation number
Differential System
Hamiltonian Systems
Linear Systems
Interval
Family

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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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 = (0 In -In 0) 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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Exponential dichotomy and rotation number for linear hamiltonian systems. / Johnson, Russell; Nerurkar, Mahesh.

In: Journal of Differential Equations, Vol. 108, No. 1, 01.01.1994, p. 201-216.

Research output: Contribution to journalArticle

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AU - Nerurkar, Mahesh

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N2 - 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 = (0 In -In 0) 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.

AB - 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 = (0 In -In 0) 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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