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Coexistence of uncountably many attracting sets for skew-products on the cylinder

The aim of this paper is to show that the existence of attracting sets for quasiperiodically forced systems can be extended to appropriate skew-products on the cylinder, homotopic to the identity, in such a way that the general system will have (at least) one attracting set corresponding to every irrational rotation number ρin the rotation interval of the base map. This attracting set is a copy of the attracting set of the system quasiperiodically forced by a (rigid) rotation of angle ρ. This shows the co-existence of uncountably many attracting sets, one for each irrational in the rotation interval of the basis.

preprint2012arXivOpen access
Lluís AlsedàSara Costa
math.DS
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Lluís AlsedàSara Costa

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