Publications Repository - Gdańsk University of Technology

We prove that with only one exception, all expanding Lorenz maps $f\colon[0,1]\to[0,1]$ with the derivative $f'(x)\ge\sqrt{2}$ (apart from a finite set of points) are locally eventually onto. Namely, for each such $f$ and each nonempty open interval $J\subset(0,1)$ there is $n\in\N$ such that $[0,1)\subset f^n(J)$. The mentioned exception is the map $f_0(x)=\sqrt{2}x+(2-\sqrt{2})/2 \pmod 1$. Recall that $f$ is an expanding Lorenz map if it is strictly increasing on $[0,c)$ and $[c,1]$ for some $c$ and satisfies the condition $\inf{f'}>1$.

Authors

• dr hab. Piotr Bartłomiejczyk link open in new tab ,
• Piotr Nowak-Przygodzki