190 research outputs found
On two-dimensional surface attractors and repellers on 3-manifolds
We show that if is an -diffeomorphism with a surface
two-dimensional attractor or repeller and is a
supporting surface for , then and
there is such that: 1) is a union
of disjoint tame surfaces such that every is
homeomorphic to the 2-torus . 2) the restriction of to
is conjugate to Anosov automorphism of
Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling
We study a system of four identical globally coupled phase oscillators with
biharmonic coupling function. Its dimension and the type of coupling make it
the minimal system of Kuramoto-type (both in the sense of the phase space's
dimension and the number of harmonics) that supports chaotic dynamics. However,
to the best of our knowledge, there is still no numerical evidence for the
existence of chaos in this system. The dynamics of such systems is tightly
connected with the action of the symmetry group on its phase space. The
presence of symmetries might lead to an emergence of chaos due to scenarios
involving specific heteroclinic cycles. We suggest an approach for searching
such heteroclinic cycles and showcase first examples of chaos in this system
found by using this approach.Comment: 18 pages, 8 figure
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