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We consider skew-products with concave interval fiber maps over a certainsubshift obtained as the projection of orbits staying in a given region. Itgenerates a new type of (essentially) coded shift. The fiber maps haveexpanding and contracting regions which dynamically interact. The dynamics alsoexhibits pairs of horseshoes of different type of hyperbolicity which, in somecases, are cyclically related.  The space of ergodic measures on the base is an entropy-dense Poulsensimplex. Those measures lift canonically to ergodic measures for theskew-product. We explain when and how the spaces of (fiber) contracting andexpanding ergodic measures glue along the nonhyperbolic ones. A key step is theapproximation (in the weak$\ast$ topology and in entropy) of nonhyperbolicmeasures by ergodic ones, obtained only by means of concavity. Concavity is notmerely a technical artificial hypothesis, but it prevents the presence ofadditional independent subsystems. The description of homoclinic relations isalso a key instrument.  These skew-products are embedded in non-decreasing entropy one-parameterfamily of diffeomorphisms stretching from a heterodimensional cycle to acollision of homoclinic classes. Associated bifurcation phenomena involve ajump of the space of ergodic measures and, in some cases, of entropy.

Mingled hyperbolicities: ergodic properties and bifurcation phenomena (an approach using concavity)