The metric entropy of endomorphisms (Q1048109)

\(M\) is a compact connected Riemannian manifold and \(f: M \rightarrow M\) is a \(C^2\) non-invertible but non-degenerate endomorphism After giving some basic notions and properties about forward Lyapunov metric, inverse limit space of (M.f), entropies in this space and partitions subordinate to the stable manifolds, the author proves that an \(f\)-invariant Borel probability measure on \(M\) satisfies an equality relating entropy, folding entropy and negative Lyapunov exponents.