  We consider families of piecewise linear maps in which the moduli of the two
slopes take different values. In some parameter regions, despite the variations
in the dynamics, the Lyapunov exponent and the topological entropy remain
constant. We provide numerical evidence of this fact and we prove it
analytically for some special cases. The mechanism is very different from that
of the logistic map and we conjecture that the Lyapunov plateaus reflect
arithmetic relations between the slopes.
