Induced subsystems associated to a Cantor minimal system

Real Coboundaries for Minimal Cantor Systems

In this paper we investigate the role of real-valued coboundaries for classifying of minimal homeomorphisms of the Cantor set. This work follows the work of Giordano, Putnam, and Skau who showed that one can use integer-valued coboundaries to characterize minimal homeomorphisms up to strong orbit equivalence. First, we prove a rigidity result. We show that there is an orbit equivalence between ...

Flow-orbit Equivalence for Minimal Cantor Systems

This paper is about ‡ow-orbit equivalence, a topological analogue of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a ‡ow-orbit equivalence. We also describe the relationship between ‡ow-orbit equivalence and a distortion function of an orbit equivalence. We show that if the ...

Minimal Cantor Systems and Unimodal Maps

Minimal Infeasible Subsystems and Benders cuts

There are many situations in mathematical programming where cutting planes can be generated by solving a certain “cut generation linear program” whose feasible solutions define a family of valid inequalities for the problem at hand. Disjunctive cuts and Benders cuts are two familiar examples. In this paper we concentrate on classical Benders cuts, as they belong to the basic toolbox for mixed-i...

A Minimal Lamination with Cantor Set-like Singularities

Given a compact closed subset M of a line segment in R, we construct a sequence of minimal surfaces Σk embedded in a neighborhood C of the line segment that converge smoothly to a limit lamination of C away from M . Moreover, the curvature of this sequence blows up precisely on M , and the limit lamination has non-removable singularities precisely on the boundary of M .