Symplectic Capacity and Periodic Motion of a Charge on a Manifold in the Magnetic211 Fields

摘要

The authors first prove that the Hofter-Zehnder symplectic capacity of a product211u001esymplectic manifold M x Z(sup 2n)(r) omega (circle plus) omega(sub 0) is less 211u001ethan or equal to the circumference for an r > 0, where Z(sup 2n)(r) is the 211u001estandard sumplectic cyclinder of radius r in Real number(sup 2n), omega(sub 0) 211u001eand (M, omega) belongs to a large class of the geometrically bounded symplectic 211u001emanifolds including monotone manifold and Calabi-Yau one. Next as applications in 211u001ethe existence of a periodic motion of a charge on a large class of manifolds 211u001eunder the action of the magnetic field and the length minimizing path among all 211u001ehomotopic one in Ham(sup c)(M, omega).