Multifractal analysis of non-uniformly hyperbolic systems

By Anders Johansson, T. Jordan, Anders Öberg, Mark Pollicott. 2008

51 citations recorded by the source corpus.

We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f0abaf63ac2f141b6d94f7219a8ee0f8b3c68500

How researchers see this paper

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In Mathematical Physics

1. G. Iommi
2. Daniel Thompson
3. T. Jordan

In Statistical and Nonlinear Physics

1. G. Iommi
2. Daniel Thompson
3. T. Jordan

Citations in the corpus

• Multifractal analysis of Birkhoff averages for countable Markov maps (2010, methodology): “Since these measures are supported on finite subsystems we can apply Lemma 2 and Lemma 3 from [16] to complete the proof.”
• A variational principle for topological pressure for certain non‐compact sets (2008, background): “In the case of the Manneville–Pomeau family of maps, the only measure with ψd μ= 0 is the Dirac measure supported at 0, and so s �→ PX(ϕ,α)(−sψ) is decreasing for α ∈L ϕ \{ 0} .B y [ 10 ], equation (5.1) holds for the same set of values, and thus Theorem 5.1 applies.”