Measures maximizing the entropy for Kan endomorphisms

In 1994, Ittai Kan provided the first examples of maps with intermingled basins. The example corresponds to a partially hyperbolic endomorphism defined on surface boundary exhibiting two physical measures. Both measures are supported boundary, and they also maximizing topological entropy. this work, we prove existence third measure in interior cylinder that maximizes entropy for larger class including example. We statement invariant large perturbations