A note about a Morse's conjecture

Authors

  • Walter T. Huaraca Vargas Departamento de Matemática da Universidade Federal de Vicosa, Brazil.

DOI:

https://doi.org/10.17268/sel.mat.2025.01.08

Keywords:

Topological Transitive, Group Action, Metrically Transitive

Abstract

In dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dimensional manifolds and prove the following two results: The conjecture is false if we do not impose restrictions on the singular set and we will prove that The Morse’s Conjecture is valid for locally free actions.

References

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Published

2025-07-26

How to Cite

Huaraca Vargas, W. T. (2025). A note about a Morse’s conjecture. Selecciones Matemáticas, 12(01), 90 - 96. https://doi.org/10.17268/sel.mat.2025.01.08

Issue

Vol. 12 No. 01 (2025): January - July

Section

Articles

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