  We study phase transitions in the thermodynamic description of
Pomeau-Manneville intermittent maps from the point of view of infinite ergodic
theory, which deals with diverging measure dynamical systems. For such systems,
we use a distributional limit theorem to provide both a powerful tool for
calculating thermodynamic potentials as also an understanding of the dynamic
characteristics at each instability phase. In particular, topological pressure
and Renyi entropy are calculated exactly for such systems. Finally, we show the
connection of the distributional limit theorem with non-Gaussian fluctuations
of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad.
Sci. USA 85, 4591 (1988)].
