Motions of the plane (shifts and rotations) correspond to automorphisms of the type I Arveson system of white noise. I prove that automorphisms corresponding to rotations cannot be extended to the type II Arveson system of Warren’s noise.

The conjugacy classes of the involutive automorphisms of the affine Kac-Moody algebras C (1) ℓ for ℓ ≥ 2 are determined using the matrix formulation of automorphisms of an affine Kac-Moody

This note gives an account of the algebraic construction of symbolic covers and representations of ergodic automorphisms of compact abelian groups. For expansive toral automorphisms this subject was initiated by A.M. Vershik.

Using McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.

In this paper, the problem formulated in [8] is solved. We prove, that the group of automorphisms of the category of free associative algebras is generated by semi-inner and mirror automorphisms.

Let Aut(X, B) be the group of all Borel automorphisms of a standard Borel space (X, B). We study topological properties of Aut(X, B) with respect to the uniform and weak topologies, τ and p, defined in [BDK1]. It is proved that the class of smooth automorphisms is dense in (Aut(X, B), p). Let Ctbl(X) denote the group of Borel automorphisms with countable support. It is shown that the topologica...