It is shown in \cite{yazar6} that a dynamical system defined by a
nonvanishing vector field on an orientable three dimensional manifold is
globally bi-Hamiltonian if and only if the first Chern class of the normal
bundle of the given vector field vanishes, and the bi-Hamiltonian structure is
globally compatible if and only if the Bott class of the complex codimension
one foliation defined by the nonvanishing vector field vanishes. In this work,
we constructed a dynamical system on S3, which is globally bi-Hamiltonian,
but the Hamiltonians are not globally compatible.Comment: 12 page