The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...

the unit group of AK but has a finer topology (using the restricted product topology ensures that a 7→ a−1 is continuous, which is not true of the subspace topology). As a topological group, IK is locally compact and Hausdorff. The multiplicative group K× is canonically embedded as a discrete subgroup of IK via the diagonal map x 7→ (x, x, x, . . .), and the idele class group is the quotient CK...

We study the affine orbifold laminations that were constructed in [LM]. An important question left open in [LM] is whether these laminations are always locally compact. We show that this is not the case. The counterexample we construct has the property that the regular leaf space contains (many) hyperbolic leaves that intersect the Julia set; whether this can happen is itself a question raised ...

be the set of affine critical values. The set Baff is a subset of B but is not necessarily equal to B. The value c ∈ C is regular at infinity if there exists a disk D centered at c and a compact set K of C2 with a locally trivial fibration f : f−1 (D) \K −→ D. There is only a finite number of non-regular values at infinity: the critical values at infinity collected in B∞. The bifurcation set B ...