Remark on Transitivity for piecewise increassing maps on R

Authors

  • Luis Bladismir Ruiz Leal Instituto de Ciencias Básicas, Universidad Técnica de Manabí, Av. Urbina y Che Guevara, Portoviejo - Ecuador.
  • Ambrosio Tineo Instituto de Ciencias Básicas, Universidad Técnica de Manabí, Av. Urbina y Che Guevara, Portoviejo - Ecuador.
  • Abdul Lugo Instituto Superior de Formación Docente Salomé Ureña, Recinto Félix Evaristo Mejía. Santo Domingo - República Dominicana.

DOI:

https://doi.org/10.17268/sel.mat.2022.01.11

Keywords:

Transitivity maps, piecewise increassing maps, vertical asymptote

Abstract

In this work a sufficient condition is shown to obtain transitivity in families of piecewise increassing maps with an inevitable discontinuity in x=0. Specifically, it is shown that the characteristics of a large class of transformations of the real line with a discontinuity in x=0 to be transitive (exhibits a dense orbit), they are the following: f has no fixed points, f has a vertical asymptote at x=0 and the preimage of zero is different from empty. In particular, the famous Boole transformation together with some of its parameterizations they exhibit these characteristics. As a particular case, for the family to a parameter of hyperbolas its dynamic behavior is explicitly determined according to the values of the parameter p > 0.

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Published

2022-07-27

How to Cite

Ruiz Leal, L. B., Tineo, A., & Lugo, A. (2022). Remark on Transitivity for piecewise increassing maps on R. Selecciones Matemáticas, 9(01), 145 - 149. https://doi.org/10.17268/sel.mat.2022.01.11

Issue

Vol. 9 No. 01 (2022): January - July

Section

Articles

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