The irregular set for maps with the specification property has full topological pressure
By Daniel Thompson. 2008
109 citations recorded by the source corpus.
Let (X, d) be a compact metric space, f : X ↦ X be a continuous map with the specification property and ϕ : X ↦ ℝ a continuous function. We consider the set of points for which the Birkhoff average of ϕ does not exist (which we call the irregular set for ϕ) and show that this set is either empty or carries full topological pressure (in the sense of Pesin and Pitskel see, for example [Y.B. Pesin, Dimension Theory in Dimensional Systems: Contemporary Views and Applications, University of Chicago Press, Chicago, 1997]). We formulate various equivalent natural conditions on ϕ that completely describe when the latter situation holds and give examples of interesting systems to which our results apply but were not previously known. As an application, we show that for a suspension flow over a continuous map with specification, the irregular set carries full topological entropy.
Subfields: Analytical Chemistry, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/23d888fab7c726d5daa05074e279ae649f3e7fdb
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In Analytical Chemistry
In Mathematical Physics
Citations in the corpus
- A variational principle for topological pressure for certain non‐compact sets (2008, methodology): “Introduction For a compact metric space (X, d), a continuous map f : X 7→ X and a continuous function φ : X 7→ R, we continue a program started in [15] to understand the topological pressure of the multifractal decomposition X = ⋃”