Dimension of measures for suspension flows

摘要

We consider hyperbolic flows and more generally suspension flows over two-sided subshifts of finite type, and establish an explicit formula for the pointwise dimension of an arbitrary measure (in particular the measure is not necessarily ergodic and it may not possess a local product structure). The applications of this formula include the description of the Hausdorff dimension of a given measure in terms of an ergodic decomposition, and the proof of the existence of measures of maximal dimension.