Instability for the rotation set of diffeomorphisms of the torus homotopic to the identity

TL;DR

This paper discusses how the closing lemma with time control can be applied to analyze the instability of the rotation set for torus diffeomorphisms homotopic to the identity, addressing a specific open question.

Contribution

It demonstrates the application of the closing lemma with time control to the problem of rotation set instability in torus diffeomorphisms.

Findings

Application of closing lemma with time control to rotation set analysis

Resolution of an open question on rotation set instability

Insights into the dynamics of torus diffeomorphisms

Abstract

The aim of this short note is to explain how the arguments of the "closing lemma with time control" of F. Abdenur and S. Crovisier (arXiv:1111.4206) can be used to answer Question 1 of the article "Instability for the rotation set of homeomorphisms of the torus homotopic to the identity" of S. Addas-Zanata.