A dynamical decomposition of the torus into pseudo-circles

TL;DR

This paper constructs a special type of irrational pseudo-rotation of the 2-torus, where fibers are pseudo-circles, using the fast-approximation method, advancing understanding of complex dynamical decompositions.

Contribution

It introduces a novel construction of a pseudo-rotation with pseudo-circle fibers, expanding the class of known dynamical systems with such properties.

Findings

Existence of a pseudo-rotation of the 2-torus with pseudo-circle fibers

Application of the fast-approximation method to this construction

Enhanced understanding of torus decompositions into complex invariant sets

Abstract

We build an irrational pseudo-rotation of the 2-torus which is semiconjugate to an irrational rotation of the circle in such a way that all the fibres of the semi-conjugacy are pseudo-circles. The proof uses the well-known `fast-approximation method' introduced by Anosov and Katok.