abstract
As a continuation of a previous work on linearization of class C1 of diffeomorphisms and flows in infinite dimensions near a fixed point, in this work we deal with the case of a saddle point with some non-resonance restrictions for the linear part. Our result can be seen as an extension of results by Hartman [Boletin de la Sociedad Matematica Mexicana 5(2), 220–241 (1960)] and Aronson, Belitskii and Zhuzhoma [Introduction to the Qualitative Theory of Dynamical systems on surfaces, AMS Transl. Math. Monog. vol.153, pp. 268–277 (1996)] in dimension two. We also present an application to a system of nonlinear wave equations.
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AMS Subject Classifications: Primary: 35B05, 34G20. Secondary: 35B40, 34D05.
Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday
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Rodrigues, H.M., Solà-Morales, J. Smooth Linearization for a Saddle on Banach Spaces. J Dyn Diff Equat 16, 767–793 (2004). https://doi.org/10.1007/s10884-004-6116-9
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DOI: https://doi.org/10.1007/s10884-004-6116-9