  It is well-known that SRB and equilibrium measures for uniformly hyperbolic
flows admit a product structure in terms of measures on stable and unstable
leaves with scaling properties given by the potential function. We describe a
construction of these leaf measures analogous to the definition of Hausdorff
measure, relying on the Pesin-Pitskel' description of topological pressure as a
dimensional characteristic using Bowen balls. These leaf measures were
constructed for discrete-time systems by the author, Ya. Pesin, and A.
Zelerowicz. In the continuous-time setting here, the description of the scaling
properties is more complete, and we use a similar procedure with two-sided
Bowen balls to directly produce the equilibrium measure itself.
