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Documents  Beresnevich, Victor | enregistrements trouvés : 2

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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 ...

11J13 ; 11J83 ; 11K60

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- 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

11J83 ; 11J13 ; 11K60 ; 28A78 ; 28A80

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