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We considered Q-state Potts model on Bethe lattice in presence of externalmagnetic field for Q<2 by means of recursion relation technique. This allows tostudy the phase transition mechanism in terms of the obtained one dimensionalrational mapping. The convergence of Feigenabaum $\alpha$ and $\delta$exponents for the aforementioned mapping is investigated for the perioddoubling and three cyclic window. We regarded the Lyapunov exponent as an orderparameter for the characterization of the model and discussed its dependence ontemperature and magnetic field. Arnold tongues analogs with winding numbersw=1/2, w=2/4 and w=1/3 (in the three cyclic window) are constructed for Q<2.The critical temperatures of the model are discussed and their dependence on Qis investigated. We also proposed an approximate method for constructing Arnoldtongues via Feigenbaum $\delta$ exponent.

Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2