Peter Raith
Universität Wien, Vienna, Austria

Let $f:[0,1]\to [0,2]$ be a continuous strictly increasing function with $f(0)$<$1$<$f(1)$. Then $T_f x:=f(x)- \left\lfloor f(x)\right\rfloor$, where $\left\lfloor y\right\rfloor$ is the largest integer smaller or equal to $y$, is called a Lorenz map. Given $\varepsilon >0$ another Lorenz map $T_{\widetilde{f}}$ (again $\widetilde{f}:[0,1]\to [0,2]$) is said to be $\varepsilon$-close to $T_f$ if $\left\|\widetilde{f}-f\right\|_{\infty}<\varepsilon$.

Continuity properties of the topological entropy and the topological entropy are investigated. In particular the topological entropy is continuous if $h_{\text{top}}(T_f)>0$. Assuming that $f$ is differentiable except on a finite set and $\inf f^{\prime}>1$ topological transitivity and topological mixing are investigated.