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Sternberg Linearization Theorem for Skew Products

Research paper by Yulij Ilyashenko, Olga Romaskevich

Indexed on: 12 May '16Published on: 10 May '16Published in: Journal of Dynamical and Control Systems



Abstract

We present a special kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears that even in the smooth case, the conjugacy is only Hölder continuous with respect to the base. The normalization theorem mentioned above may be applied to perturbations of skew products and to the study of new persistent properties of attractors.