Harvesting dynamic aspects from a real rational map : the bulb of period 5

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This work is a small, but strong, contribute to understand better the behavior, under iteration, of the Real Rational Map, f(x)=(x²-a)/(x²-b), with 0<b<a<1, with a and b real parameters. So, we show in this work how to choose some suitable regions of the parameter space (a,b), that allows a controlled and efficient study of this kind of maps, using some classical dynamical systems tools as the critical point orbit, Lyapunov exponents and their relation with the bifurcation diagram of the map.