An anti-classification theorem for minimal homeomorphisms on the torus

TL;DR

This paper proves that minimal homeomorphisms on the torus cannot be classified up to topological conjugacy using countable structures, highlighting fundamental limitations in their classification.

Contribution

It establishes an anti-classification theorem demonstrating the impossibility of classifying minimal torus homeomorphisms via countable models.

Findings

Proves the non-classifiability of minimal torus homeomorphisms

Shows limitations of countable structures in topological dynamics

Highlights fundamental complexity in classifying minimal systems

Abstract

We show that it is impossible to classify topological conjugacy relation of minimal homeomorphisms on the torus by countable structures.