Zobrazeno 1 - 10 of 78 pro vyhledávání: '"Sinai, Yakov G"'
1
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Ergodic Properties of Square-Free Numbers
Autor: Cellarosi, Francesco, Sinai, Yakov G.
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This implies that thi
Externí odkaz: http://arxiv.org/abs/1112.4691
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2
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Non-Standard Limit Theorems in Number Theory
Autor: Cellarosi, Francesco, Sinai, Yakov G.
We present a limit theorem describing the behavior of a probabilistic model for square-free numbers. The limiting distribution has a density that comes from the Dickman-De Bruijn function and is constant on the interval $[0,1]$. We also provide estim
Externí odkaz: http://arxiv.org/abs/1010.0035
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3
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Separating Solution of a Quadratic Recurrent Equation
Autor: Sinai, Yakov G., Vinogradov, Ilya
Publikováno v: Journal of Statistical Physics, Volume 136, Number 4 / August, 2009
In this paper we consider the recurrent equation $$\Lambda_{p+1}=\frac1p\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda_{q}\Lambda_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and $\Lambda_1=y>0$ given. We give conditions on $f$ that guarantee the existen
Externí odkaz: http://arxiv.org/abs/0812.0776
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4
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A Limit Theorem for Birkoff sums of non-integrable functions over rotations
Autor: Sinai, Yakov G., Ulcigrai, Corinna
We consider Birkhoff sums of functions with a singularity of type 1/x over rotations and prove the following limit theorem. Let $S_N= S_N(\alpha,x)$ be the N^th non-renormalized Birkhoff sum, where $x in [0,1)$ is the initial point, $\alpha\in [0,1)$
Externí odkaz: http://arxiv.org/abs/0710.1287
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5
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Renewal-type Limit Theorem for the Gauss Map and Continued Fractions
Autor: Sinai, Yakov G., Ulcigrai, Corinna
In this paper we prove the following renewal-type limit theorem. Given an irrational $\alpha$ in (0,1) and R>0, let $q_{n_R}$ be the first denominator of the convergents of $\alpha$ which exceeds R. The main result in the paper is that the ratio $q_{
Externí odkaz: http://arxiv.org/abs/0710.1283
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6
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Structure Theorem for (d,g,h)-Maps
Autor: Kontorovich, Alex V., Sinai, Yakov G.
Publikováno v: Bulletin of the Brazilian Mathematical Society, Volume 33, Issue 2, Jul 2002, Pages 213 - 224
The (3x+1)-Map, T, acts on the set, Pi, of positive integers not divisible by 2 or 3. It is defined by T(x) = (3x+1)/2^k, where k is the largest integer for which T(x) is an integer. The (3x+1)-Conjecture asks if for every x in Pi there exists an int
Externí odkaz: http://arxiv.org/abs/math/0601622
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8
Akademický článek
Nonsymmetric bifurcations of solutions of the 2D Navier–Stokes system
Autor: Li, Dong, Sinai, Yakov G.
Publikováno v: In Advances in Mathematics 2012 229(3):1976-1999
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