A Minimax Selector for a Class of Hamiltonians on Cotangent Bundles
نویسنده
چکیده
We construct a minimax selector for eventually quadratic hamiltonians on cotangent bundles. We use it to give a relation between Hofer’s energy and Mather’s action minimizing function. We also study the local flatness of the set of twist maps.
منابع مشابه
Periodic Orbits for Hamiltonian systems in Cotangent Bundles
We prove the existence of at least cl(M) periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M . These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M . We discretize the variational problem by decomposing the time 1 map into a product of “symplectic twist ...
متن کاملTruncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space
Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...
متن کاملExact Lagrangian Submanifolds in Simply-connected Cotangent Bundles
We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology....
متن کاملThree approaches towards Floer homology of cotangent bundles
Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set, one can define Floer homology and show that it is naturally isomorphic to singular homology of the free loop space. We review the three isomorphisms construc...
متن کاملOn the Floer homology of cotangent bundles
This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T M of a compact orientable manifold M . The first result is a new L estimate for the solutions of the Floer equation, which allows to deal with a larger and more natural class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Fl...
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 1999