Generalized Whittaker's equations for holonomic mechanical systems.
Global existence for the Hamilton-Jacobi equations in Hilbert space
GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type
We describe both the classical lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
GO++: A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of geometric optics type
We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
Hamilton-Jacobi theory and moving frames.
Infinitesimal symplectic relations and generalized hamiltonian dynamics
Invariance of global solutions of the Hamilton-Jacobi equation
We show that every global viscosity solution of the Hamilton-Jacobi equation associated with a convex and superlinear Hamiltonian on the cotangent bundle of a closed manifold is necessarily invariant under the identity component of the group of symmetries of the Hamiltonian (we prove that this group is a compact Lie group). In particular, every Lagrangian section invariant under the Hamiltonian flow is also invariant under this group.
Le problème de Cauchy pour les équations de Hamilton-Jacobi-Bellman
On a Hamilton-Jacobi equation
On some completions of the space of hamiltonian maps
In one of his papers, C. Viterbo defined a distance on the set of Hamiltonian diffeomorphisms of endowed with the standard symplectic form . We study the completions of this space for the topology induced by Viterbo’s distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances that allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous...
On The Canonical Formalisam With The Derivates Of Higher Order
On the canonical formalism with the derivatives of higher order.
On the real singularities of the N-body problem.
On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics
We study the zero-temperature limit for Gibbs measures associated to Frenkel–Kontorova models on . We prove that equilibrium states concentrate on configurations of minimal energy, and, in addition, must satisfy a variational principle involving metric entropy and Lyapunov exponents, a bit like in the Ruelle–Pesin inequality. Then we transpose the result to certain continuous-time stationary stochastic processes associated to the viscous Hamilton–Jacobi equation. As the viscosity vanishes, the...
Optimal control problems with upper semicontinuous Hamiltonians
In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value function is...
Optimal investment under stochastic volatility and power type utility function
2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.
Parabolic perturbations of Hamilton–Jacobi equations
We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.
Pursuit in physical spaces
Regularity of solutions of the Hamilton-Jacobi equation
Resurgence in a Hamilton-Jacobi equation
We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. We derive the Bridge equation, which encompasses infinitely many resurgent relations satisfied by the formal solution and the other components of the formal integral.