We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the " twisted " Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry....

We analyze Euclidean spheres in higher dimensions and the corresponding orbit equivalence relations induced by group of rational rotations from viewpoint descriptive set theory. It turns out that such are not treeable dimension greater than 2. Then we show rotation relation n ⩾ 5 $n \geqslant 5$ is Borel reducible to one any lower dimension. Our methods combine a cocycle superrigidity result wo...

Abstract The construction of a spectral cocycle from the case one-dimensional substitution flows [A. I. Bufetov and B. Solomyak. A for systems translation flows. J. Anal. Math. 141 (1) (2020), 165–205] is extended to setting pseudo-self-similar tilings in ${\mathbb R}^d$ , allowing expanding similarities with rotations. pointwise upper Lyapunov exponent this used bound local dimension measures ...

The main objective of this article is to analyse the dynamics of Burgers equation on the unit interval, driven by multiplicative white noise. It is shown that the solution field of the stochastic Burgers equation generates a smooth perfect and locally compacting cocycle on the energy space L2([0, 1],R). Using multiplicative ergodic theory techniques, we compute the discrete non-random Lyapunov ...

By considering the way an n-tuple of points in the 2-disk are linked together under iteration of an orientation preserving diffeomorphism, we construct a dynamical cocycle with values in the Artin braid group. We study the asymptotic properties of this cocycle and derive a series of topological invariants for the diffeomorphism which enjoy rich properties.

Relations will be described between the quandle cocycle invariant and the minimal number of colors used for non-trivial Fox colorings of knots and links. In particular, a lower bound for the minimal number is given in terms of the quandle cocycle invariant.

In this paper we prove an upper semicontinuity result for perturbations of cocycle attractors. In particular, we study relationship between non-autonomous and global attractors. In this sense, we show that the concept of a cocycle attractor is a sensible generalization to non-autonomous and random dynamical systems of that of the global attractor.