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The dynamical properties of exciton transfer coupled to polarizationvibrations in a two site system are investigated in detail. A fixed pointanalysis of the full system of Bloch - oscillator equations representing thecoupled excitonic - vibronic flow is performed. For overcritical polarization abifurcation converting the stable bonding ground state to a hyperbolic unstablestate which is basic to the dynamical properties of the model is obtained. Thephase space of the system is generally of a mixed type: Above bifurcation chaosdevelops starting from the region of the hyperbolic state and spreading withincreasing energy over the Bloch sphere leaving only islands of regulardynamics. The behaviour of the polarization oscillator accordingly changes fromregular to chaotic.Comment: uuencoded compressed Postscript file containing text and figures. In  case of questions, please, write to schanz@summa.physik.hu-berlin.de

Excitonic-vibronic coupled dimers: A dynamic approach