Triple collisions of invariant bundles
Jordi-Lluís Figueras Àlex Haro
Discrete & Continuous Dynamical Systems - B 2013, 18(8): 2069-2082 doi: 10.3934/dcdsb.2013.18.2069
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.
keywords: Oseledets theory. Nonuniformly hyperbolic linear skew-products
A note on the fractalization of saddle invariant curves in quasiperiodic systems
Jordi-Lluís Figueras Àlex Haro
Discrete & Continuous Dynamical Systems - S 2016, 9(4): 1095-1107 doi: 10.3934/dcdss.2016043
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.
keywords: Breakdown of saddle invariant curves quasiperiodic systems.

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