Semigroups of real functions with dense orbits

Abstract

Let ${\mathcal{F}}_I=\{f:I\to I|f(x)=(Ax+B)/(Cx+D);AD-BC\ne 0\}$, where $I$ is an interval. For $x\in I$, let ${\Omega }_x$ be the orbit of $x$ under the action of the semigroup of functions generated by $f,g\in {\mathcal{F}}_I$. Our main result in this paper is to describe all $f,g\in {\mathcal{F}}_I$ such that ${\Omega }_x$ is dense in $I$ for all $x$.

18 pages

References in corpus (1)

• Affine actions of a free semigroup on the real line