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### Open Access Journals

DCDS-B

We provide several explicit examples of 3D quasiperiodic
linear skew-products with simple Lyapunov spectrum, that is with
$3$ different Lyapunov multipliers, for which the corresponding Oseledets bundles
are measurable but not continuous, colliding in a measure zero dense set.

DCDS-S

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.

## Year of publication

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