Volume 4 (2008) Issue 1

Abstract: Let \(k\) be a field and \(\overline{k}\) an algebraic closure of \(k\). The paper is devoted to the description of subrings of the Lie ring \(sl_{2}overline{k}\) that contain an abelian subring which is a one-dimensional subspace of the \(k\)-vector space \(sl_{2}overline{k}\).

Abstract: Barnsley’s formula for the attractor of a hyperbolic IFS with condensation is generalized for the omega-limit set of a weakly contracting set-valued map with eventual condensation. The latter need not be a contraction, as well as its omega-limit set need not be an attractor.