The topological development of the last geometric Poincare theorem

In 1925, G. Birkhoff generalized the last geometric Poincare’s theorem (1912), rejecting the area preserving assumption. This Birkhoff’s paper initiated intensive investigations in the direction of the Poincare theorem topological version development, proceeding till nowadays, that are motivated, besides pure mathematical importance, by a necessity to obtain a tool for establishing the existence of periodic solutions of differential equations. The history of these investigations is concerned with such names as L.E.J. Brouwer, B. de Kerékjarto, J.Franks, P.Carter and others.