We prove two continuity theorems for the Lyapunov exponents of the maximal entropy measure of polynomial automorphisms of C. The first continuity result holds for any family of polynomial automorphisms of constant dynamical degree. The second result is the continuity of the upper exponent for families degenerating to a 1-dimensional map.

The paper presents useful invariants of resolutions of cyclic STS(v) with v ≤ 39, namely of all resolutions of cyclic STS(15), STS(21) and STS(27), of the resolutions with nontrivial automorphisms of cyclic STS(33) and of resolutions with automorphisms of order 13 of cyclic STS(39). 2010 MSC: 05B07, 05E18

a Supported in part by \Ministrstvo za znanost in tehnologijo Slovenije", proj.no. Abstract The problem of lifting automorphisms of a (fairly arbitrary) topological space to automorphisms of a covering space is studied by means of voltage groups. To this end we introduce some required background results regarding group actions and covering spaces.

We investigate some situation in which automorphisms of a groupG are uniquely determined by their restrictions to a proper subgroup H . Much of the paper is devoted to studying under which additional hypotheses this property forces G to be nilpotent if H is. As an application we prove that certain countably infinite locally nilpotent groups have uncountably many (outer) automorphisms.

In this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms. 2000 Mathematics subject classification: primary 20D45; secondary 16S34.

We prove that the group of automorphisms of the Lie algebra DerK(Pn) of derivations of a polynomial algebra Pn = K[x1, . . . , xn] over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the polynomial algebra Pn.

We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of one-dimensional solenoids, a complete description is given and the problem of determining the range of certain invariants of topological conjugacy is discussed. Several new results and old and new open problems are de...

In this paper it is established that all two-dimensional polynomial automorphisms over a Dedekind Q-algebra are stably tame; in fact, they become tame with the addition of three more dimensions. A key element in the proof is this additional new theorem: Over an Artinian Q-algebra all two-dimensional polynomial automorphisms having Jacobian determinant one are tame.

Let A be a finite dimensional division algebra (not necessarily associative) over a field. The automorphisms of A having order three are characterized by giving a canonical matrix representation for each of the possible types (there are three). Examples are given to show that each type does exist. Some general results concerning automorphisms of prime power order are included.

We bound the nuclear dimension of crossed products associated to some partial actions finite groups or Z on dimensional locally compact Hausdorff second countable spaces. Our results apply globalizable actions, group minimal automorphisms, and automorphisms acting zero-dimensional spaces, a class one containing 1-dimensional CW complexes. This extends work global systems by Hirshberg Wu.