Combinatorics

Attractor

Pure mathematics

Mathematics

Mathematical analysis

Gibbs measure

Hausdorff dimension

Iterated function system

Transitive relation

Measure (data warehouse)

Computer science

Bounded function

Hausdorff measure

Database

Journal of Modern Dynamics

We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a unique equilibrium measure. Our method is to use tools from geometric measure theory to construct a suitable family of reference measures on unstable leaves as a dynamical analogue of Hausdorff measure, and then show that the averaged pushforwards of these measures converge to a measure that has the Gibbs property and is the unique equilibrium measure.

Equilibrium measures for some partially hyperbolic systems