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For geometrically finite non-compact developable hyperbolic orbisurfaces(including those of infinite volume), we provide transfer operator familieswhose Fredholm determinants are identical to the Selberg zeta function. Ourproof yields an algorithmic and uniform construction. This construction isinitiated with an externally provided cross section for the geodesic flow onthe considered orbisurface that yields a highly faithful, but non-uniformlyexpanding discrete dynamical system modelling the geodesic flow. Through anumber of algorithmic steps of reduction, extension, translation, induction andacceleration, we turn this cross section into one that yields a still highlyfaithful, but now uniformly expanding discrete dynamical system. The arisingtransfer operator family is nuclear of order zero on suitable Banach spaces. Inaddition, finite-dimensional twists with non-expanding cusp monodromy can beincluded.

Selberg zeta functions, cuspidal accelerations, and existence of strict transfer operator approaches