  We construct combinatorial Hubbard trees for all unicritical polynomials, and
for all exponential maps, for which the critical (singular) value does not
escape. More precisely, out of an external angle, or more generally a kneading
sequence, we construct a forward invariant tree for which the critical orbit
has the given kneading sequence.
  When the critical orbit of a unicritical polynomial is periodic or
preperiodic, then the existence of a Hubbard tree is classical. Our trees exist
even when the critical orbit is infinite (in many cases, this yields infinite
trees), and even when the polynomial Julia set fails to be path connected. In
the latter case, our trees cannot be reconstructed from the Julia set in
complex dynamics. Our trees also exist for kneading sequences that do not arise
in complex dynamics (for non complex-admissible kneading sequences).
