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Sternberg linearization theorem for skew products

Research paper by Yulij Ilyashenko, Olga Romaskevich

Indexed on: 27 Aug '15Published on: 27 Aug '15Published in: Mathematics - Dynamical Systems



Abstract

We present a new 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 H\"older 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.