# Multiple Rotation Type Solutions for Hamiltonian Systems on $T^ell imesmathbb{R}^{2n-ell}$ - Mathematics > Symplectic Geometry

Multiple Rotation Type Solutions for Hamiltonian Systems on $T^ell imesmathbb{R}^{2n-ell}$ - Mathematics > Symplectic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: This paper deals with multiplicity of rotation type solutions for Hamiltoniansystems on $T^\ell\times \mathbb{R}^{2n-\ell}$. It is proved that, for everyspatially periodic Hamiltonian system, i.e., the case $\ell=n$, there exist atleast $n+1$ geometrically distinct rotation type solutions with given energyrotation vector. It is also proved that, for a class of Hamiltonian systems on$T^\ell\times\mathbb{R}^{2n-\ell}$ with $1\leqslant\ell\leqslant 2n-1$ but$\ell eq n$, there exists at least one periodic solution or $n+1$ rotationtype solutions on every contact energy hypersurface.

Author: ** Hui Qiao**

Source: https://arxiv.org/