Tri-Coble surfaces and their automorphisms

We construct some positive entropy automorphisms of rational surfaces with no periodic curves. The in question, which we term tri-Coble surfaces, are blow-ups \begin{document}$ \mathbb P^2$\end{document} at 12 points have contractions down to three different Coble surfaces. arise as compositions lifts Bertini involutions from certain degree id="M2">\begin{document}$1$\end{document} weak del Pezzo