  In this paper we study the future asymptotics of spatially homogeneous
Bianchi type II cosmologies with a tilted perfect fluid with a linear equation
of state. By means of Hamiltonian methods we first find a monotone function for
a special tilted case, which subsequently allows us to construct a new set of
monotone functions for the general tilted type II cosmologies. In the context
of a new partially gauge invariant dynamical system, this then leads to a proof
for a theorem that for the first time gives a complete description of the
future asymptotic states of the general tilted Bianchi type II models. The
generality of our arguments suggests how one can produce monotone functions
that are useful for determining the asymptotics of other tilted perfect fluid
cosmologies, as well as for other sources.
