Almost reducibility of quasiperiodic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>S</mml:mi><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-cocycles in ultradifferentiable classes

Chatal, Maxime; Chavaudret, Claire

doi:10.1016/j.jde.2023.01.041

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“…Later, many authors ( [3][4][5][6][7][8][9][10][11][12]) paid attention to the reducibility for the following quasiperiodic linear system:…”

Section: Introductionmentioning

confidence: 99%

Onthe Reducibility of a Class Nonlinear Almost Periodic Hamiltonian Systems

Xue,

Sun

2024

Symmetry

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Inthis paper, we consider the reducibility of a class of nonlinear almost periodic Hamiltonian systems. Under suitable hypothesis of analyticity, non-resonant conditions and non-degeneracy conditions, by using KAM iteration, it is shown that the considered Hamiltonian system is reducible to an almost periodic Hamiltonian system with zero equilibrium points for most small enough parameters. As an example, we discuss the reducibility and stability of an almost periodic Hill’s equation.

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“…Later, many authors ( [3][4][5][6][7][8][9][10][11][12]) paid attention to the reducibility for the following quasiperiodic linear system:…”

Section: Introductionmentioning

confidence: 99%