Given a factor map p : (X, T )→ (Y, S) of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups K0(X)/K0(Y ) in terms of intermediate extensions which are extensions of (Y, S) by a compact abelian group. Then we show that, by contrast, the existence of an intermediate non-a...

We classify C-orderable groups admitting only finitely many C-orderings. We show that if a C-orderable group has infinitely many C-orderings, then it actually has uncountably many C-orderings, and none of these is isolated in the space of C-orderings. As a relevant example, we carefully study the case of Baumslag-Solitar’s group B(1, 2). We show that B(1, 2) has four C-orderings, each of which ...

We introduce two new characterizations of Meyer sets. A repetitive Delone set in R with finite local complexity is topologically conjugate to a Meyer set if and only if it has d linearly independent topological eigenvalues, which is if and only if it is topologically conjugate to a bundle over a d-torus with totally disconnected compact fiber and expansive canonical action. “Conjugate to” is a ...

For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space Zα such that indZα = α, and no closed subset L of Zα with indL less than the predecessor of α is a partition in Zα. An α-dimensional Cantor Ind-manifold can be constructed similarly.

We prove Whitney regularity results for the solutions of the coboundary equation over dynamically defined Cantor sets satisfying a natural geometric regularity condition, in particular hyperbolic basic sets in dimension two. To do this we prove an analogue of Journé’s well-known result in the context of Cantor sets satisfying geometric regularity conditions.

The period doubling Cantor sets of strongly dissipative Hénon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the period doubling Cantor sets of two-dimensional Hénon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, e.g. the onedimensional case. The other extreme...