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For topologically mixing locally expanding semigroup actions generated by afinite collection of $C^{1+\alpha}$ conformal local diffeomorphisms, we providea countable Markov partition satisfying the finite images and the finite cycleproperties. We show that they admit inducing schemes and describe the towerconstructions associated with them. An important feature of these towers isthat their induced maps are equivalent to a subshift of countable type. Throughthe investigating the ergodic properties of induced map,we prove the existenceof liftable measures and establish a thermodynamic formalism of the inducedskew product with respect to them.

Locally Expanding Actions: Markov Partition and Thermodynamic of the induced skew product