A variational principle for topological pressure for certain non‐compact sets
By Daniel Thompson. 2008
66 citations recorded by the source corpus.
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:limn→∞1n∑i−0n−1φ(fi(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.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/62cb3e6c26d784772057f7475d57b82e9fb5cf9c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- The irregular set for maps with the specification property has full topological pressure (2008, background): “gif"/> (we consider the topological pressure of the sets X (ϕ, α) in 1 ).”