Differentiability with respect to parameters in global smooth linearization

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• 作者：Hildebrando M. Rodrigues^a ; ^{hmr@icmc.usp.br} ; J. Solà ; -Morales^b ; ^{jc.sola-morales@upc.edu}
• 关键词：Linearization ; Conjugacy ; Smooth dependence on parameters
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：262
• 期：6
• 页码：3583-3596
• 全文大小：264 K
• 卷排序：262

文摘

Let XX be a Banach space and Tθ:X→XTθ:X→X a family of invertible contractions, Tθ=Lθ+fθTθ=Lθ+fθ, where LθLθ is linear and fθfθ is nonlinear with fθ(0)=0fθ(0)=0. We give conditions for the existence of a family of global linearization maps HθHθ, such that Hθ∘Tθ∘Hθ−1=Lθ, with a smooth dependence on θ. The results depend strongly on the choice of some appropriate spaces of maps, adapted norms and the use of a specific fixed point theorem with smooth dependence on parameters.