Radiation reaction, renormalization and Poincaré symmetry.
Randomly forced vibrations of a string
Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension
We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint -pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable complex window, provided that the...
Realisation of rendezvous by the transfer orbit which is tangential to the original and terminal orbits
Recent progress in the integration of Poisson systems via the mid-point rule and Runge-Kutta algorithm.
Recherches analytiques d'un cas de rotation d'un solide autour d'un point fixe
Reconfiguration in the attitude control of icosahedral bodies
Reconstruction of the satellite orbit via orientation angles.
Reconstruction phases for Hamiltonian systems on cotangent bundles.
Réductibilité de systèmes dynamiques variationnels
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric
For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...
Reductions and conservation laws for BBM and modified BBM equations
In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation...
Regular and chaotic motion of a bush-shaft system with tribological processes.
Regularity of solutions of the Hamilton-Jacobi equation
Regularity of weak KAM solutions and Mañé’s Conjecture
We provide a crash course in weak KAM theory and review recent results concerning the existence and uniqueness of weak KAM solutions and their link with the so-called Mañé conjecture.
Relations between constants of motion and conserved functions
We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.
Relations between distributions of random vibratory processes and distributions of their envelopes
Relativistische Mechanik mit klassicher Geometrie und Kinematik.
Réponse à la Note de M. Allégret sur le Problème des trois corps.