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A normal form theorem for Brjuno skew-systems through renormalization
- J. Differential Equations
"... Abstract. We develop a dynamical renormalization method for the problem of local reducibility of analytic linear quasi-periodic skew-product flows on T 2 ×SL(2, R). This approach is based on the continued fraction expansion of the linear base flow and deals with ’small-divisors ’ by turning them int ..."
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Cited by 4 (2 self)
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Abstract. We develop a dynamical renormalization method for the problem of local reducibility of analytic linear quasi-periodic skew-product flows on T 2 ×SL(2, R). This approach is based on the continued fraction expansion of the linear base flow and deals with ’small-divisors ’ by turning them into ’large-divisors’. We use this method to give a new proof of a normal form theorem for a Brjuno base flow. 1.
LOCAL CONJUGACY CLASSES FOR ANALYTIC TORUS FLOWS
"... Abstract. If a real-analytic flow on the multidimensional torus close enough to linear has a unique rotation vector which satisfies an arithmetical condition Y, then it is analytically conjugate to linear. We show this by proving that the orbit under renormalization of a constant Y vector field attr ..."
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Cited by 1 (1 self)
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Abstract. If a real-analytic flow on the multidimensional torus close enough to linear has a unique rotation vector which satisfies an arithmetical condition Y, then it is analytically conjugate to linear. We show this by proving that the orbit under renormalization of a constant Y vector field attracts all nearby orbits with the same rotation vector. 1.
