On the coexistence of irreducible orbits of coincidences for multivalued admissible maps on the circle via Nielsen theory

The present paper can be regarded as a natural, significant, multivalued extension of some results matching the general periodic point theory (like the celebrated Sharkovsky-type theorems) and the standard Nielsen fixed point theory. Concretely, the coexistence of irreducible orbits of coincidences is established for multivalued circle maps by means of Nielsen-type topological invariants. A well known theorem for single-valued maps, obtained independently by Efremova [1] and Block et al. [2], is nontrivially generalized in this way. Some further possibilities for admissible maps on tori are indicated. Several illustrative examples are supplied. The crucial idea is based on detecting the kind of a complete isomorphism between periodic points of associated single-valued maps and irreducible orbits of coincidences of given multivalued admissible maps on tori.