Random-walk scaling without Bernoulli statistics: transport, persistence and resonances in the triangle map

The triangle map is an area-preserving, piecewise-parabolic map of the torus with vanishing Lyapunov exponent. We study the symbolic process $X_n=\pm1$ given by the two halves of the torus, whose partial sums $S_n$ are the transport of the lifted momentum, with an integrator free of accumulated roun