This is a preview. Log in through your library . Abstract We prove that almost no numbers in Cantor's middle-thirds set are very well approximable by rationals. More generally, we discuss Diophantine ...

Without the theorem of the excluded middle, all kinds of difficulties arise. In fact, many mathematical proofs are based on this very principle. It is no surprise, then, that only a few mathematicians ...

More precisely, we prove that if the sum of the Hausdorff dimensions of two regular Cantor sets is bigger than one then, in almost all cases, there are translations of them whose intersection ...

Cantor minimal systems arise naturally through constructions such as substitutions and odometers, where iterative processes generate rich and often counterintuitive behaviour.

Dynamical systems provide a rigorous framework for understanding the evolution of complex systems over time, encapsulating models ranging from classical mechanical systems to chaotic and fractal ...