The embedding problems aim to describe when a certain map f (homeomorphism, diffeomorphism, etc) 

on a topological space X can be embedded in a flow with the same regularity.  There are fundamental contributions  

to the embedding problem for both the setting of homeomorphisms in low dimension (one and two) and diffeomorphisms 

dated from the fifties and the sixties, due to Anderson, Andrea, Foland, Fort, Palis, Utz and Zdun among others. 

    One bridge bridge between this problem from Topology and Dynamical Systems is the centralizer of the dynamical system 

generated by the map, which can be used to create obstructions for a map not to embed in a flow. We propose a different 

approach to the embedding problem for homeomorphisms and prove that ´most' homeomorphisms do not embed in 

continuous flows using topological invariants, as topological entropy and rotation sets. This is a joint work with 

Wescley Bonomo (Federal University of Espírito Santo - Brazil).