On the reducibility of a class of finitely differentiable quasi-periodic linear systems

Li, Jia; Zhu, Chunpeng

doi:10.1016/j.jmaa.2013.10.077

Cited by 21 publications

(6 citation statements)

References 11 publications

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“…The previous papers mainly considered the reducibility of analytic quasi-periodic systems. In fact, some similar results also hold true for finitely smooth quasiperiodic systems; see [7].…”

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confidence: 54%

On the reducibility of a class of almost periodic Hamiltonian systems

Li¹,

Xu²

2021

DCDS-B

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In this paper we consider the following linear almost periodic hamiltonian systemẋ = (A + εQ(t, ε))x, x ∈ R 2 , where A is a constant matrix with different eigenvalues, and Q(t, ε) is analytic almost periodic with respect to t and analytic with respect to ε. Without any non-degeneracy condition, we prove that the linear hamiltonian system is reducible for most of sufficiently small parameter ε by an almost periodic symplectic mapping. 2020 Mathematics Subject Classification. 37J40.

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“…The previous papers mainly considered the reducibility of analytic quasi-periodic systems. In fact, some similar results also hold true for finitely smooth quasiperiodic systems; see [7].…”

mentioning

confidence: 54%

On the reducibility of a class of almost periodic Hamiltonian systems

Li¹,

Xu²

2021

DCDS-B

Self Cite

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“…Junxiang [8] obtained the similar result for the multiple eigenvalue case. Later, many authors [7][8][9][10] paid attention to the reducibility of the quasiperiodic linear system (1), which is close to a constant coefficient linear system.…”

Section: Introductionmentioning

confidence: 99%

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

Xue

Zhao

2020

Journal of Function Spaces

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In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Qt. Applications to the Schrödinger equation are also given.

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“…Recently, many authors [20][21][22][23] considered the reducibility of the following system which is close to constant coefficients matrix:̇= ( + ( )) .…”

Section: Introductionmentioning

confidence: 99%

On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

Xue

Zhao

2018

Journal of Function Spaces

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In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this system can be reduced to y˙=A⁎ε+εR⁎t,εy, ε∈0,ε⁎, where R⁎ is exponentially small in ε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies as Q.

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On the reducibility of a class of finitely differentiable quasi-periodic linear systems

Cited by 21 publications

References 11 publications

On the reducibility of a class of almost periodic Hamiltonian systems

On the reducibility of a class of almost periodic Hamiltonian systems

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

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