Projective transformations of rotation sets

TL;DR

This paper presents a new proof and extension of a result showing that certain projective transformations of rotation sets of torus homeomorphisms are also realizable as rotation sets, broadening understanding of their geometric properties.

Contribution

It provides a new proof and extends Kwapisz's result on the realizability of projectively transformed rotation sets for torus homeomorphisms.

Findings

Projective transformations preserve the realizability of rotation sets.

Extended class of transformations under which rotation sets remain realizable.

Enhanced understanding of the geometric structure of rotation sets.

Abstract

We give a new proof and extend a result of J. Kwapisz: whenever a set C is realized as the rotation set of some torus homeomorphism, the image of C under certain projective transformations is also realized as a rotations set.