High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
نویسندگان
چکیده
Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which have quadratic growth in the velocities or in the momenta. Such results are based on the richness of the topology of the space of curves satisfying the given boundary conditions. In this note we show how these results can be extended to the classical setting of Tonelli Lagrangians (Lagrangians which are C-convex and superlinear in the velocities), or to Hamiltonians which are superlinear in the momenta and have a coercive action integrand.
منابع مشابه
Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملSmooth critical sub-solutions of the Hamilton-Jacobi equation
We establish the existence of smooth critical sub-solutions of the HamiltonJacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union of finitely many hyperbolic periodic orbits or fixed points. Let M be a compact manifold without boundary. A function H(x, p) : T M −→ R is called a Tonelli ...
متن کاملOptimal transportation on non-compact manifolds
In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type dr , r > 1, where d is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.
متن کاملOn generic properties of lagrangians on surfaces: the Kupka-Smale theorem
In this work, we consider generic properties of lagrangians. Our main result is the Theorem of Kupka-Smale, in the lagrangian setting, claiming that, for a fixed value fixed k ∈ R, generically (in Mañé sense, that is, there exists a residual subset (in C topology) of smooth potentials, O, such that L+f have the desired property, for all f ∈ O), for a convex and superlinear lagrangian defined in...
متن کاملThe concentration function problem for $G$-spaces
In this note, we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$. We prove a necessary and sufficient condition for the concentration functions of a spread-out irreducible probability measure $mu$ on $G$ to converge 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 2006