TY - JOUR AU - Rudyak, Yuli B. AU - Tralle, Aleksy PY - 1999/12/01 Y2 - 2024/03/29 TI - On symplectic manifolds with aspherical symplectic form JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 14 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.1999.038 SP - 353 - 362 AB - We consider closed symplectically aspherical manifolds, i.e. closed symplectic manifolds $(M,\omega)$ satisfying the condition$[\omega]|_{\pi_2M}=0$. Rudyak and Opre[< i> On the Lustrnik–Schnirelmann category of symplecticmanifolds and the Arnold conjecture< /i> , Math. Z. < b> 230< /b> (1999), 673–678] remarked that suchmanifolds have nice and controllable homotopy properties. Now it is clear that these properties are mostly determined by the fact that the strict category weight of $[\omega]$ equals 2. We apply the theory of strict category weight to the problem of estimating the number ofclosed orbits of charged particles in symplectic magnetic fields. In case of symplectically aspherical manifolds our theory enables us to improve some known estimations. ER -