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# Documents  Beresnevich, Victor | enregistrements trouvés : 2

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## Simultaneous rational approximations to several functions of a real variable Beresnevich, Victor | CIRM H

Multi angle

Research talks

As is well known, simultaneous rational approximations to the values of smooth functions of real variables involve counting and/or understanding the distribution of rational points lying near the manifold parameterised by these functions. I will discuss recent results in this area regarding lower bounds for the Hausdorff dimension of $\tau$-approximable values, where $\tau\geq \geq 1/n$ is the exponent of approximations. In particular, I will describe a very recent development for non-degenerate maps as well as a recently introduced simple technique based on the so-called Mass Transference Principle that surprisingly requires no conditions on the functions except them being $C^2$. As is well known, simultaneous rational approximations to the values of smooth functions of real variables involve counting and/or understanding the distribution of rational points lying near the manifold parameterised by these functions. I will discuss recent results in this area regarding lower bounds for the Hausdorff dimension of $\tau$-approximable values, where $\tau\geq \geq 1/n$ is the exponent of approximations. In particular, I will ...

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## Measure theoretic laws for lim sup sets Beresnevich, Victor ; Dickinson, Detta ; Velani, Sanju | American Mathematical Society 2006

Ouvrage

- 91 p.
ISBN 978-0-8218-3825-9

Memoirs of the american mathematical society , 0846

Localisation : Collection 1er étage

approximation diophantienne # probabilité # mesure de Hausdorff # fractale # théorème de Khintchire # théorème de Jornit # loi zéro-un

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Ressources Electroniques (Depuis le CIRM)

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