5 research outputs found
Lattice isomorphisms of bisimple monogenic orthodox semigroups
Using the classification and description of the structure of bisimple
monogenic orthodox semigroups obtained in \cite{key10}, we prove that every
bisimple orthodox semigroup generated by a pair of mutually inverse elements of
infinite order is strongly determined by the lattice of its subsemigroups in
the class of all semigroups. This theorem substantially extends an earlier
result of \cite{key25} stating that the bicyclic semigroup is strongly lattice
determined.Comment: Semigroup Forum (published online: 15 April 2011
Partial symmetry breaking and heteroclinic tangencies
We study some global aspects of the bifurcation of an equivariant family of
volume-contracting vector fields on the three-dimensional sphere. When part of
the symmetry is broken, the vector fields exhibit Bykov cycles. Close to the
symmetry, we investigate the mechanism of the emergence of heteroclinic
tangencies coexisting with transverse connections. We find persistent suspended
horseshoes accompanied by attracting periodic trajectories with long periods