A Nielsen theory for coincidences of iterates

TL;DR

This paper develops a Nielsen theory for coincidences of iterates of two self maps on closed manifolds, aiming to generalize Nielsen periodic point theory despite various challenges.

Contribution

It introduces a Nielsen framework for coincidences of iterates, extending classical Nielsen periodic point theory to a broader context with new theoretical insights.

Findings

Provides a Nielsen theory for coincidences of iterates

Achieves results similar to classical Nielsen periodic point theory under stronger conditions

Addresses obstacles in generalizing Nielsen theory to coincidence problems

Abstract

As the title suggests, this paper gives a Nielsen theory of coincidences of iterates of two self maps f, g of a closed manifold. The ideas is, as much as possible, to generalize Nielsen type periodic point theory, but there are many obstacles. Many times we get similar results to the "classical ones" in Nielsen periodic point theory, but with stronger hypotheses.