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The object of the present paper is to give a qualitative description of the bifurcation
mechanisms associated with a closed invariant curve in three-dimensional maps, leading to
its doubling, not related to a standard doubling of tori. We propose an explanation on how
a closed invariant attracting curve, born via Neimark-Sacker bifurcation, can be
transformed into a repelling one giving birth to a new attracting closed invariant curve
which has doubled...
This work contributes to classify the dynamic behaviors of piecewise smooth systems in
which characterize the qualitative changes
in the dynamics. A central point of our investigation is the intersection of two border
collision bifurcation curves in a parameter plane. This problem is also associated with
the continuity breaking in a fixed point of a piecewise smooth map. We will relax the
hypothesis needed in [4] where it was proved that in the case...
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