Regular components of homeomorphisms of the $n$-dimensional sphere

In this paper the structure of the regular components of homeomorphisms of the $n$-dimensional sphere is studied. Results are obtained which turn out to describe the possible types of regular components, and which generalize to dimensions $n\geqslant3$ the results of Birkhoff and Smith in dimension $2$. As applications we describe the regular components of structurally stable diffeomorphisms of $S^n$ with a finite number of periodic points and the connected components of orbitally stable trajectories of a structurally stable dynamical system on $S^n$ with a finite number of closed trajectories.
Bibliography: 6 titles.