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Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation

Giuseppe Da Prato, Arnaud Debussche (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup P t φ does exist for any bounded φ ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.

Diffusion times and stability exponents for nearly integrable analytic systems

Pierre Lochak, Jean-Pierre Marco (2005)

Open Mathematics

For a positive integer n and R>0, we set B R n = x n | x < R . Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian h r = 1 2 r 1 2 + . . . 1 2 r n - 1 2 + r n on 𝕋 n × B R n , with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of 𝕋 n × B R n , and setting ε j : = h - H j C 0 ( V ) the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface,...

Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics

Alexandru Oană, Mircea Neagu (2012)

Communications in Mathematics

In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.

Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff

Maria Letizia Bertotti, Sergey V. Bolotin (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as t ± , to an «equilibrium at infinity». This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity.

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