2008/09/23 by Daniel Thompson · 39 citations
Mathematics · Physics and Astronomy · #Compact space #Continuous map #Dimension (graph theory) #Geometric Analysis and Curvature Flows #Interval (graph theory) #Mathematical Dynamics and Fractals #Multifractal system #Real line #Spectrum (functional analysis) #Statistical Mechanics and Entropy #Topological entropy #Variational principle #math.DS #msc:37C45
paper · pdf · doi:10.1112/jlms/jdp041
published in Journal of the London Mathematical Society 80(3), 585-602 (Wiley)
arxiv created 2008/09/23 · openalex publication_date 2009/09/04 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let (X, d) be a compact metric space, let f:X ↦ X be a continuous map with the specification property and let φ: X ↦ ℝ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form x ∈ X : lim n → ∞ 1 n ∑ i − 0 n − 1 φ ( f i ( x ) ) = α Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification and the dimension spectrum of certain non-uniformly expanding interval maps.