We study a family of H-to-1 conservative ergodic endomorphisms which we will show to admit no rj-finite absolutely continuous invariant measure. We exhibit recurrent measures for these transformations and study their ratio sets; the examples can be realized as C°° endomorphisms of the 2-torus.

The relative ranks of the monoid of endomorphisms of a strong independence algebra of infinite rank modulo two distinguished subsets are calculated. These subsets are the group of automorphisms and the endomorphisms α satisfying α2 = α. The extra generators are characterised in each case. 2000 Mathematics Subject Classification. 20M20, 08A35.

We consider families of E0-semigroups continuously parametrized by a compact Hausdorff space, which are cocycle-equivalent to a given E0-semigroup β. When the gauge group of β is a Lie group, we establish a correspondence between such families and principal bundles whose structure group is the gauge group of β. Let H be a Hilbert space, which we will always assume to be separable and infinitedi...

We construct two practical algorithms for twisted conjugacy classes of polycyclic groups. The first algorithm determines whether elements a group are conjugate given endomorphisms, under the condition that their Reidemeister coincidence number is finite. second representatives endomorphisms if finite, or returns “false” this infinite. also discuss theoretical extension these to polycyclic-by-fi...

There are six classes of endomorphisms for a graph. The sets these form chain under the inclusion sets. In order to systematically study endomorphisms, Böttcher and Knauer defined concepts endomorphism spectrum type graph in 1992. this paper, based on property structure monoids graphs, double-edge fan graphs described. particular, we give spectra types graphs.

This note is a sequel to [7] where we investigated the endomorphisms of a certain class of Banach algebras of infinitely differentiable functions on the unit interval. Start with a perfect, compact plane setX. We say that a complex-valued function f defined on X is complex-differentiable at a point a ∈ X if the limit f (a) = lim z→a, z∈X f(z)− f(a) z − a exists. We call f ′(a) the complex deriv...