Solenoidal endomorphisms minimize topological entropy

摘要

The entropy conjecture was settled for tori in 1977 by Misiurewicz and Przytycki (Bull. Acad. Polon. Sci. Sr. Sci. Math. Astronom. Phys. 25 575-8). We show that their result extends from tori to finite-dimensional compact and connected abelian groups. We give stronger results for hyperbolic automorphisms.