  We present an analytical method to solve Dyson's hierarchical model,
involving the scaling variables near the high-temperature fixed point. The
procedure seems plagued by the presence of small denominators as in
perturbative expansions near integrable systems in Hamiltonian mechanics.
However, in all cases considered, a zero denominator always comes with a zero
numerator. We conjecture that these cancellations occur in general, suggesting
that the model has remarkable features reminiscent of the integrable systems.
