A decomposition theorem for the space of -smooth skew products with complicated dynamics of the quotient map

Abstract

We use the notions of the -function and functions suitable to it, to give a detailed proof of a decomposition theorem for the space of -smooth skew products of interval maps whose quotient maps have complicated dynamics and satisfy the additional condition of -stability with respect to the -norm. In our theorem, the space of -smooth skew products is decomposed into a union of four nonempty, pairwise disjoint subspaces. We give examples of maps contained in each of the four subspaces.Bibliography: 46 titles.