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A note on the fractalization of saddle invariant curves in quasiperiodic systems

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  • The purpose of this paper is to describe a new mechanism of destruction of saddle invariant curves in quasiperiodically forced systems, in which an invariant curve experiments a process of fractalization, that is, the curve gets increasingly wrinkled until it breaks down. The phenomenon resembles the one described for attracting invariant curves in a number of quasiperiodically forced dissipative systems, and that has received the attention in the literature for its connections with the so-called Strange Non-Chaotic Attractors. We present a general conceptual framework that provides a simple unifying mathematical picture for fractalization routes in dissipative and conservative systems.
    Mathematics Subject Classification: Primary: 37G35, 37C55; Secondary: 37D45.

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