# Metric techniques for convex stationary ergodic Hamiltonians

## Related Articles

- A Characterization of the Existence of Solutions for Hamilton-Jacobi Equations in Ergodic Control Problems with Applications. Arisawa, M.; Ishii, H.; Lions, P.-L. // Applied Mathematics & Optimization;2000, Vol. 42 Issue 1, p35
We give a characterization of the existence of bounded solutions for Hamilton-Jacobi equations in ergodic control problems with state-constraint. This result is applied to the reexamination of the counterexample given in [5] concerning the existence of solutions for ergodic control problems in...

- Variational Solutions of Coupled Hamilton--Jacobi Equations. Loreti, P.; Vergara Caffarelli, G. // Applied Mathematics & Optimization;2000, Vol. 41 Issue 1, p9
Abstract. In this note we study variational solutions of weakly coupled Hamilton-Jacobi equations in the case where the Hamiltonians are convex. More precisely, we build the variational solution by an approximation scheme.

- When is a Hamiltonian system separable? Marshall, Ian; Wojciechowski, Stefan // Journal of Mathematical Physics;Jun88, Vol. 29 Issue 6, p1338
The Hamiltonian system given by H= 1/2 p2+V(q) with VâˆˆCâˆž(Rn) is considered. A method for integrating such a system is that of separating the variables in the Hamiltonâ€“Jacobi equation. It is known that if such a separation is possible, then it can take place only when the...

- Integrable systems based on SU(p,q) homogeneous manifolds. del Olmo, M. A.; Rodríguez, M. A.; Winternitz, P. // Journal of Mathematical Physics;Nov93, Vol. 34 Issue 11, p5118
The general theory of the separation of variables in Hamiltonâ€“Jacobi and Laplaceâ€“Beltrami equations on the SU(p,q) hyperboloid is used to introduce completely integrable Hamiltonian systems on O(p,q) hyperboloids. Each of the q+1 different Cartan subalgebras of su(p,q) leads to a...

- A class of Liouville-integrable Hamiltonian systems with two degrees of freedom. McLenaghan, Raymond G.; Smirnov, Roman G. // Journal of Mathematical Physics;Oct2000, Vol. 41 Issue 10
A class of two-dimensional Liouville-integrable Hamiltonian systems is studied. Separability of the corresponding Hamilton-Jacobi equation for these systems is shown to be equivalent to other fundamental properties of Hamiltonian systems, such as the existence of the Lax and bi-Hamiltonian...

- Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data. Lio, Francesca; Ley, Olivier // Applied Mathematics & Optimization;Jun2011, Vol. 63 Issue 3, p309
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+| x|) at...

- Tensor formulation of Hamiltonâ€™s equations. Lim, Paul H. // Journal of Mathematical Physics;Sep88, Vol. 29 Issue 9, p2001
Hamiltonâ€™s equations are presented in manifestly covariant form. The resulting equations of motion are solved via a covariant Hamiltonâ€“Jacobi scheme. A covariant correspondence principle is introduced, and it is employed to quantize the equations.

- On the dynamics of singular, continuous systems. Güler, Y. // Journal of Mathematical Physics;Apr89, Vol. 30 Issue 4, p785
The Hamiltonâ€“Jacobi theory of a special type of singular continuous systems is investigated by the equivalent Lagrangians method. The Hamiltonian is constructed in such a way that the constraint equations are involved in the canonical equations implicitly. The Hamiltonâ€“Jacobi...

- Fast Marching Method for Calculating Reactive Trajectories for Chemical Reactions. Stuart Bothwell; Paul Ayers // Journal of Mathematical Chemistry;Jan2007, Vol. 41 Issue 1, p1
We present a method for computing classical Newtonian trajectories that minimize the path length or transit time from reactant to product. Our approach is based on a generalization of the fast-marching method, which allows us to construct the solution of the Hamilton-Jacobi equation for the...