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We identify a class of hyperbolic transcendental entire maps and we provethat some of its elements generate a class of potentials for which exhibit aconformal and invariant probability Gibbs measure. The methods and techniquesfrom the thermodynamic formalism can be extended to this class of potentials.To complement this study we highlight that the dynamics of such a map on somesubset of the Julia set is conjugated to the shift map over a code space withcountable alphabet and the euclidean metric on the complex plane induces ametric on the symbolic space which is not compatible with the shift standardmetric. From this fact, we provide a general description of the thermodynamicformalism from symbolic dynamic outlook, by studying the shift map acting on anon-compact and invariant subset of the full shift space with a countablyinfinite alphabet and a class of weakly H\"older continuous potentials, toprove the existence of a conformal and absolutely continuous invariantprobability measure.

On the existence of a conformal and an absolutely continuous invariant measure for transcendental entire maps