Displaying similar documents to “Weight-balanced measures and free energy for one-dimensional dynamics.”

Operator-valued version of conditionally free product

Wojciech Młotkowski (2002)

Studia Mathematica

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We present an operator-valued version of the conditionally free product of states and measures, which in the scalar case was studied by Bożejko, Leinert and Speicher. The related combinatorics and limit theorems are provided.

Physical measures for infinite-modal maps

Vítor Araújo, Maria José Pacifico (2009)

Fundamenta Mathematicae

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We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they...

Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Nikolay Tzvetkov, Nicola Visciglia (2013)

Annales scientifiques de l'École Normale Supérieure

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Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.