Documents  11J83 | enregistrements trouvés : 13

ISBN 978-3-540-52190-7

Lecture notes in mathematics , 1415

Localisation : Collection 1er étage

polynome

10C08 ; 11J81 ; 11J82 ; 11J83 ; 11J85

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Research talks;Number Theory

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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Research talks

This is a survey on progress in metric discrepancy theory and probabilistic aspects in harmonic analysis. We start with classical limit theorems of Salem and Zygmund as well as with the work of Erdoes and Gaal and of Walter Philipp. A focus lies on laws of the iterated logarithm for discrepancy functions of lacunary sequences. We show the connection to certain diophantine properties of the underlying lacunary sequences obtaining precise asymptotic formulas. Different phenomena for subexponentially growing, for exponentially growing and for superexponentially growing sequences are established. Furthermore, relations to arithmetic dynamical systems and to Donald Knuth`s concept of pseudorandomness are discussed. Recent results are contained in joint work with Christoph Aistleitner and Istvan Berkes and it is planed to publish parts of it in a Jean Morlet Springer lecture Notes volume. This is a survey on progress in metric discrepancy theory and probabilistic aspects in harmonic analysis. We start with classical limit theorems of Salem and Zygmund as well as with the work of Erdoes and Gaal and of Walter Philipp. A focus lies on laws of the iterated logarithm for discrepancy functions of lacunary sequences. We show the connection to certain diophantine properties of the underlying lacunary sequences obtaining precise ...

11K38 ; 11J83 ; 11K60

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- 147 p.
ISBN 978-0-521-20461-3

Localisation : Ouvrage RdC (BAKE)

fonction elliptique # forme linéaire dans les logarithmes # théorie des nombres transcendants # théorie métrique

11J83 ; 11J86 ; 11J89 ; 11Jxx

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- vii; 77 p.
ISBN 978-1-4704-4095-4

Memoirs of the American Mathematical Society , 1276

Localisation : Collection 1er étage

approximation diophantienne multiplicative # expansion d'Ostrowski # distribution uniforme

11K60 ; 11J71 ; 11A55 ; 11J83 ; 11J20 ; 11J70 ; 11K38 ; 11J54 ; 11K06 ; 11K50

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- x; 243 p.
ISBN 978-2-85629-313-3

Panoramas et synthèses , 0032

Localisation : Collection 1er étage

Approximation diophantienne # arbres aléatoires # cascade multiplicative # chaos multiplicatif # chaîne de Markov # dimension de boîte # dimension de Hausdorff # dimension de packing # fonction multifractale # formalisme multifractal # fractals # fragmentation aléatoire # martingales # mesure multifractale # mesures # processus de branchement # produits de Riesz # recouvrements # régularité ponctuelle # spectre multifractal # systèmes dynamiques # ubiquité Approximation diophantienne # arbres aléatoires # cascade multiplicative # chaos multiplicatif # chaîne de Markov # dimension de boîte # dimension de Hausdorff # dimension de packing # fonction multifractale # formalisme multifractal # fractals # fragmentation aléatoire # martingales # mesure multifractale # mesures # processus de branchement # produits de Riesz # recouvrements # régularité ponctuelle # spectre multifractal # systèmes dynamiques ...

11J83 ; 11K06 ; 26A15 ; 26A30 ; 28A78 ; 28A80 ; 37B40 ; 43A25 ; 60G18 ; 60J80

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- 156 p.
ISBN 978-0-470-26706-6

Scripta series in mathematics

Localisation : Ouvrage RdC (SPRI)

approximation diophantienne # métrique

11J83 ; 11Jxx ; 11K60

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- 297 p.
ISBN 978-0-19-850083-4

London mathematical society monographs new series , 0018

Localisation : Ouvrage RdC (HARM)

algorithmique # distribution # expansion # irrégularité de distribution # mesure de dimension de Hausdorff # métrique # théorie des nombres # théorie probabiliste

11J83 ; 11K38 ; 11K50 ; 11K55

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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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- xiii; 191 p.
ISBN 978-3-11-043941-0

De Gruyter graduate

Localisation : Ouvrage RdC (KESS)

théorie ergodique infinie # système dynamique # mesure de Gauss # fraction continue # suite de Farey # fonction point d'interrogation

37-02 ; 11-02 ; 37A45 ; 11J70 ; 11K50 ; 11K55 ; 37Axx ; 11B57 ; 11J83 ; 60K05

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- v; 137 p.
ISBN 978-1-4704-2886-0

Memoirs of the American Mathematical Society , 1215

Localisation : Collection 1er étage

géométrie hyperbolique # groupe hyperbolique # approximation diophantienne # jeu de Schmidt

11J83 ; 20H10 ; 28A78 ; 37F35

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- 168 p.

Cambridge tracts in mathematics and mathematical physics , 0045

Localisation : Collection 1er étage

approximation diophantienne # approximation homogène # approximation inhomogène # approximation rationnelle des nombres algébriques # chaine de Markov # distribution uniforme # nombre de Pisot-Vijayaraghavan # théorème de transférence # théorie métrique

11J04 ; 11J68 ; 11J83 ; 11Jxx

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