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In this paper, we look at the following question. We consider cellularautomata in the hyperbolic plane, (see Margenstern, 2000, 2007 and Margenstern,Morita, 2001) and we consider the global function defined on all possibleconfigurations. Is the injectivity of this function undecidable? The problemwas answered positively in the case of the Euclidean plane by Jarkko Kari, in1994. In the present paper, we show that the answer is also positive for thehyperbolic plane: the problem is undecidable.

On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)