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Some implications of absolute geometries in the description of complex systems dynamics, at various scale resolutions are highlighted. In such context, by means of an analytic geometry of 2 x 2 matrices, a generalization of the standard velocities space in Fock's sense is obtained. Moreover, in the one-dimensional homographic action case, various chaos transition scenarios (period doubling and intermittences) can be mimed, through the selection of scale resolution.