We present a dynamical analog of the Mordell-Lang conjecture for integral points. We are able to prove this conjecture in the case of endomorphisms of semiabelian varieties.

In what follows we shall present certain results concerning the lifting property of a space L°°(Z, ju), where Z is locally compact and 11 a positive measure on Z. We shall discuss several applications and state several problems. Most of the results which will be presented here were jointly obtained by A. lonescu Tulcea and the author, during the last few years. Some of these results have alread...

We give an estimate for the Hausdorff dimension of the bifurcation locus of a family of endomorphisms of Pk(C). This dimension is maximal near isolated Lattès examples.

We consider expansive group actions on a compact metric space containing special fixed point denoted by [Formula: see text], and endomorphisms of such systems whose forward trajectories are attracted toward text]. Such called asymptotically nilpotent, we study the conditions in which they that is, map entire to text] finite number iterations. show for large class discrete groups, this property ...

It should be noted that the definition (introduced in [l]) of a normal endomorphism of a loop G is radically different from the usual definition for groups. Nevertheless (as shown in [2]) the two definitions are equivalent when G is a group. In particular, the present theorem generalizes one of Heerema [3]. We may add that in [2], by assuming that the loop G was Moufang, we were able to be much...

has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] is “very big”. More precisely, if f is a polynomial of degree n ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then End(J(C)) = Z. Notice that it easily follows that the ring of K-endomorphisms of J(C) coincides with Z and the real pro...

An abelian surface A over a field K has potential quaternionic multiplication if the ring End K̄ (A) of geometric endomorphisms of A is an order in an indefinite rational division quaternion algebra. In this brief note, we study the possible structures of the ring of endomorphisms of these surfaces and we provide explicit examples of Jacobians of curves of genus two which show that our result is...

A monic endomorphism of a structure A can be extended to an automorphism uf a larger structure A We investigate which properties are preserved by this process.

In a first order language we interpret the action of monoid M embeddings (ℚ,<) on set ℚ inside (M,°). A similar result is proved for E all endomorphisms (ℚ,≤).