On the Failure of Linearization for Germs of C^1 Hyperbolic Vector Fields in Dimension One
Journal of Dynamics and Differential Equations(2023)
摘要
We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, C^1 and C^1+ac settings.
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关键词
Vector field,Diffeomorphism,Hyperbolicity,Linearization
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