Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.