In this work, we demonstrate that the integral formula for a generalised Sato-Levine invariant is consistent in certain situations with Evans and Berger's fourth-order winding number. Also, found that, principle, one can derive analogous high-order numbers by which calculate entanglement of braids. The number Brunnian 4-braid calculated algebraically using cup product on cohomology finite regul...

In this paper, we investigate the stochastic Cahn–Hilliard–Navier–Stokes equations in two-dimensional spaces. Applying Maslowski–Seidler method, establish existence of invariant measure state space [Formula: see text] with weak topology. We also prove global pathwise solutions using compactness argument.

A general construction for ?nite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of f n () will imply the existence of a ?nite invariant measure for the map f which is absolutely continuous with respect to , a measure on the phase space describing the sets of measure zero. Furthermore we will discuss ...