In this paper, decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system xn+1=f(xn;r), being f an unimodal function. We prove a theorem, which states the necessary and sufficient conditions for the break-up of compound orbits in their simpler constituents. A corollary to this theorem provides an algorithm for the computation of those orbits. This process closes the theoretical framework initiated in [J. San Martín, M.J. Moscoso, A. González Gómez, Composition law of cardinal ordering permutations, Physica D, 239:1135–1146, 2010. Theorem 2 of present work closes the theoretical frame of composition and decomposition.
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