**MSC:**- 30C55 General theory of univalent and multivalent functions
- 32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30), {For functions of several hypercomplex variables, See 30G35}

polynomial-like maps f, we

prove that on a certain interval, which contains the

interval (0,\HD(J(f))), the pressure function

t -> P(-t\log|f'|) is real-analytic.

Our results generalize the work of Makarov and Smirnov.