Geometry, dynamics and thermodynamics

We consider the micro-canonical ensemble of classical Hamiltonian mechanics from a geometric and dynamical point of view. We show how various thermodynamic quantities may be calculated within the micro-canonical ensemble itself, without making explicit, reference to the canonical ensemble. We rederive formulas by Lebowitz et al (5) and Pearson et al (6), relating e.g. specific heat to fluctuations in the kinetic energy