In this section, we will consider the case when the Hamiltonian H(x)
is autonomous. For the sake of simplicity, we shall also assume that it
is C1.
We shall first consider the question of nontriviality, within the
general framework of #math8##tex2html_wrap_inline718#A∞, B∞#tex2html_wrap_inline719#-subquadratic Hamiltonians. In
the second subsection, we shall look into the special case when H is
#math9##tex2html_wrap_inline722#0, b∞#tex2html_wrap_inline723#-subquadratic, and we shall try to derive additional
information.