Periodic Orbits near Symplectic Submanifolds
نویسندگان
چکیده
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this implies the existence of contractible periodic orbits for a dense set of low energy values.
منابع مشابه
Periodic Orbits of Hamiltonian Flows near Symplectic Critical Submanifolds
In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of the motion of a charged low energy particle on a Riemannian manifold under the influence of a magnetic field.
متن کاملSymplectic Homology and Periodic Orbits near Symplectic Submanifolds
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...
متن کاملMaslov Class Rigidity for Lagrangian Submanifolds via Hofer’s Geometry
In this work, we establish new rigidity results for the Maslov class of Lagrangian submanifolds in large classes of closed and convex symplectic manifolds. Our main result establishes upper bounds for the minimal Maslov number of displaceable Lagrangian submanifolds which are product manifolds whose factors each admit a metric of negative sectional curvature. Such Lagrangian submanifolds exist ...
متن کاملOn the Special Role of Symmetric Periodic Orbits in a Chaotic System
After early work of Hénon it has become folk knowledge that symmetric periodic orbits are of particular importance. We reinforce this belief by additional studies and we further find that invariant closed symplectic submanifolds caused by discrete symmetries prove to be an important complement to the long known role of the orbits. The latter have particular importance in semi-classics. Based on...
متن کاملPeriodic Orbits of Hamiltonian Flows near Symplectic Extrema
For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence of energy levels converging to zero.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002