Exponential decay of correlations and Lyapunov exponents

Let $f$ be a non-uniformly expanding map. An orbit has a zero Lyapunov exponent if its Lyapunov exponent is zero, and $f$ has exponential decay of correlations if its correlations decay exponentially. Exponential-decay conjecture. The map $f$ has exponential decay of correlations if and only if it has no orbits with zero Lyapunov exponent. This heuristic conjecture proposes that zero-Lyapunov-exponent orbits are precisely the obstruction to exponential mixing for non-uniformly expanding maps; the source does not establish either implication.