Uniqueness of the measure of maximal entropy for the squarefree flow
By Ryan Peckner. Israel Journal of Mathematics, 2012
51 citations recorded by the source corpus.
The squarefree flow is a natural dynamical system whose topological and ergodic properties are closely linked to the behavior of squarefree numbers. We prove that the squarefree flow carries a unique measure of maximal entropy and express this measure explicitly in terms of a skew-product of a Kronecker and a Bernoulli system. Using this characterization and a number-theoretic argument, we then show that the unique maximum entropy measure fails to possess the Gibbs property.
Subfields: Condensed Matter Physics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0fc351282a038068140384d372807fb7686d0adf
How researchers see this paper
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In Condensed Matter Physics
- J. Kułaga-Przymus
- Gerhard Keller
- el Houcein el Abdalaoui
- Mariusz Lemanczyk
- Thierry de la Rue
- Christoph Richard
In Mathematical Physics
- J. Kułaga-Przymus
- Mariusz Lemanczyk
- el Houcein el Abdalaoui
- Thierry de la Rue
- Gerhard Keller
- Christoph Richard
- C. Liverani
- Terence Tao
Citations in the corpus
- Dynamics on the graph of the torus parametrization (2015, methodology): “For this particular example, its simplex of invariant probability measures is quite well understood [45, 34].”
- A dynamical point of view on the set of B-free integers (2013, methodology): “This generalizes the formula given by Sarnak [12] in the context of the square-free flow, a proof of which can be found in [11].”
- The Chowla and the Sarnak conjectures from ergodic theory point of view (2014, background): “Moreover, for any block C appearing in z(2), ν(C) > 0 (for z = μ, see [22] and for the general case, see [3]).”