Yakov G. Sinai

Blow ups of complex solutions of the 3D NavierStokes system and renormalization group method

We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on

Ergodic properties of square-free numbers

R^3

Renewal-type Limit Theorem for the Gauss map and continued fractions

. We show that there exists an open set in the space of

Non-standard Limit Theorems in Number Theory

10

Singularities of complex-valued solutions of the two-dimensional Burgers system

-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time. Keywords: Navier-Stokes system, renormalization group theory, fixed point, linearization near the fixed point, spectrum of the linearized group, Hermite polynomials

NAVIER–STOKES SYSTEM ON THE FLAT CYLINDER AND UNIT SQUARE WITH SLIP BOUNDARY CONDITIONS

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 this system is not weakly mixing and has zero measure-theoretical entropy.

Distribution of Energy Levels of Quantum Free Particle on the Liouville Surface and Trace Formulae

In this paper we prove the following renewal-type limit theorem. Given an irrational

A Brief Introduction to Dynamical Zeta Functions

\alpha

Fractal properties of critical invariant curves

in (0,1) and R>0, let

Bifurcations of Solutions of the 2-Dimensional Navier–Stokes System

q_{n_R}