Una nota sobre transitividad de transformaciones crecientes a trozos sobre R

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.

Año de publicación:

2022

Keywords:

Fuente:

google