Remark on Transitivity for piecewise increassing maps on R

• Autores: Ruiz Leal, Luis Bladismir, Tineo, Ambrosio, Lugo, Abdul
• Formato: artículo
• Fecha de Publicación: 2022
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/3483
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3483
• Nivel de acceso: acceso abierto
• Materia: Transitivity maps; piecewise increassing maps; vertical asymptote; Funciones transitivas; funciones crecientes por partes; asíntota vertical

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.