TY - JOUR
AU - Ruiz Leal, Luis Bladismir
AU - Tineo, Ambrosio
AU - Lugo, Abdul
PY - 2022/07/27
Y2 - 2024/06/12
TI - Remark on Transitivity for piecewise increassing maps on R
JF - Selecciones Matemáticas
JA - Sel.Mat.
VL - 9
IS - 01
SE -
DO - 10.17268/sel.mat.2022.01.11
UR - https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3483
SP - 145 - 149
AB - <p>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.</p>
ER -