  We construct an example of a Hamiltonian flow $f^t$ on a $4$-dimensional
smooth manifold $\mathcal{M}$ which after being restricted to an energy surface
$\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic
dynamics that is there is an open and dense $f^t$-invariant subset
$U\subset\mathcal{M}_e$ such that the restriction $f^t|U$ has non-zero Lyapunov
exponents in all directions (except the direction of the flow) and is a
Bernoulli flow while on the boundary $\partial U$, which has positive volume
all Lyapunov exponents of the system are zero.
