On a Problem in Diophantine Approximation
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
math.NT↗
arXiv subjects
Yakov Sinai
Publications and source records attributed to Yakov Sinai.
Blow Ups of Complex Solutions of the 3D-Navier-Stokes System
We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on $R^3$. We show that there exists an open set in the space of 10-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.
physics.flu-dyn↗
Statistical (3x+1) -- problem
Take an odd number x >0. Then 3x+1 is even and one can find an integer k> 0 so that y= 3x+1/2^k is again odd. We get in this way the mapping T, Tx=y. The paper contains two theorems describing statistical properties of T. The first describes statistical properties of trajectories for large x. The second gives some information about the probability distribution appearing in this problem.
math.DS↗