2018/10/31 by Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Bounded function #Bundle #Control and Stability of Dynamical Systems #Dynamical systems theory #Gibbs measure #Hausdorff measure #Iterated function system #Mathematical Dynamics and Fractals #Measure (data warehouse) #Property (philosophy) #Theoretical and Computational Physics #Transitive relation #math.DS #msc:37C40 #msc:37C45 #msc:37D30 #msc:37D35
paper · pdf · doi:10.3934/jmd.2020006
published as Journal of Modern Dynamics, 16 (2020), 155-205 · The published version of this paper contains an error in the proof of Lemma 6.6, which is corrected here (the lemma remains correct as stated). arXiv admin note: text overlap with arXiv:1803.10374
openalex created_date 2018/10/26 · openalex publication_date 2020/01/01 · arxiv created 2020/12/23 · arxiv updated 2020/12/24 · openalex updated_date 2026/08/05
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.