Abstract

In 1974 Michael Shub asked the following question: When the topological entropy of a continuous mapping of a compact manifold into itself is estimated from below by the logarithm of the spectral radius of the linear mapping induced in the cohomologies with real coefficients? This estimate has been called the Entropy Conjecture. In 1977 Misiurewicz and Przytycki proved that the Entropy Conjecture holds for all continuous mappings on tori. Here we prove the Entropy Conjecture for all continuous maps of compact nilmanifolds.