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We show that a behaviour analogous to degenerate hyperbolicity can occur innearest-neighbour cellular automata (CA) with three states. We construct a3-state rule by "lifting" elementary CA rule 140. Such "lifted" rule isequivalent to rule 140 when arguments are restricted to two symbols, otherwiseit behaves as identity. We analyze the structure of multi-step preimages of 0,1 and 2 under this rule by using minimal finite state machines (FSM), andexploit regularities found in these FSM. This allows to construct explicitexpressions for densities of 0s and 1s after $n$ iterations of the rulestarting from Bernoulli distribution. When the initial Bernoulli distributionis symmetric, the densities of all three symbols converge to their stationaryvalues in linearly-exponential fashion, similarly as in finite-dimensionaldynamical systems with hyperbolic fixed point with degenerate eigenvalues.

An example of degenerate hyperbolicity in a cellular automaton with 3 states