This paper was published as Nonlinearity, 2009, 22 (7), pp. 1663-1672. It is available from http://iopscience.iop.org/0951-7715/22/7/010/. Doi: 10.1088/0951-7715/22/7/010Metadata only entryThe 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
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