Some Physical Implications Of Absolute Geometries In The Description Of Complex Systems Dynamics

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.