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We consider MRL maps (Markov-Renyi-L\"uroth), a class of interval maps withinfinitely many branches that can have parabolic fixed points. We prove thatfor every MRL map $T$, the Lyapunov spectrum can be expressed in terms of theLegendre transform of the topological pressure of $-t\log|T'|$, generalizingprevious results in the area. We also show that the Lyapunov spectrum coincideswith a function directly related to the Newton-Raphson method applied to thetopological pressure of $-t\log|T'|$.

The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps