Multiple periodic points of the Poincaré map of Lagrangian systems on tori (Q1974146)

This paper deals with the Lagrangian system \[ {d \over dt} L_{\dot x}(t, x,\dot x)- L_x(t,x,\dot x)=0,\quad x\in\mathbb{R}^n\tag{1} \] with \(L(t,x,p)= {1\over 2} A(x)p\cdot p+ V(t,x)\), where \(A\) is positive definite, symmetric, \(A\) and \(V\) are \(C^3\) and \(1\)-periodic in all of their variables. The author proves that the Poincaré map of (1) possesses infinitely many periodic points on \(T^n\) produced by contractible integer periodic solutions.