This paper revisits one of the rst models of analog computation, the
General Purpose Analog Computer (GPAC). In particular, we restrict our
attention to the improved model presented in [11] and we show that it
can be further re ned. With this we prove the following: (i) the previous
model can be simpli ed; (ii) it admits extensions having close connec-
tions with the class of smooth continuous time dynamical systems. As a
consequence, we conclude that some of these extensions achieve Turing
universality. Finally, it is shown that if we introduce a new notion of
computability for the GPAC, based on ideas from computable analysis,
then one can compute transcendentally transcendental functions such as
the Gamma function or Riemann's Zeta function