2014/08/31 by Xueting Tian
Chemistry · Mathematics · #Chromatography in Natural Products #Combinatorics #Computer science #Dynamical system (definition) #Dynamical systems theory #Entropy (arrow of time) #Ergodic theory #Finite set #Function (biology) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Mixing (physics) #Physics #Pure mathematics #Set (abstract data type) #Subshift of finite type #Topological entropy #Type (biology) #math.DS #msc:37B10 #msc:37B20 #msc:37B40 #msc:37D20 #msc:37D25 #msc:54H20
paper · pdf · doi:10.3934/dcds.2017118
published as Discrete and Continuous Dynamical System-Series A, Volume 37 (5), 2745-2763 (2017) · The title "Joint Birkhoff Ergodic Average and Topological Pressure" is changed by "Topological Pressure for the Completely Irregular Set of Birkhoff Averages"
openalex publication_date 2017/01/01 · arxiv created 2017/02/24 · arxiv updated 2017/02/27 · openalex created_date 2017/03/03 · openalex updated_date 2026/08/05
It is well-known that for certain dynamical systems (satisfying specification or its variants), the set of irregular points w.r.t. a continuous function φ (i.e. points with divergent Birkhoff ergodic averages observed by φ ) either is empty or carries full topological entropy (or pressure, see [6,17,36,37] etc. for example). In this paper we study the set of irregular points w.r.t. a collection D of finite or infinite continuous functions (that is, points with divergent Birkhoff ergodic averages simultaneously observed by all φ∈D ) and obtain some generalized results. As consequences, these results are suitable for systems such as mixing shifts of finite type, uniformly hyperbolic diffeomorphisms, repellers and β- shifts.