11 citations · 54 across the 16 of their papers we have counts for
16 papers
On the local and global properties of the gravitational spheres of influence
D. Souami, J. Cresson, C. Biernacki +1
We revisit the concept of sphere of gravitational activity, to which we give both a geometrical and physical meaning. This study aims to refine this concept in a much broader conte…
Selection of a Stochastic Landau-Lifshitz Equation and the Stochastic Persistence Problem
Jacky Cresson, Yasmina Kheloufi, Khadra Nachi +1
In this article, we study the persistence of properties of a given classical deter-ministic dierential equation under a stochastic perturbation of two distinct forms: external and…
A Time scales Noether's theorem
Baptiste Anerot, Jacky Cresson, Frédéric Pierret
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as we…
Scale dynamical origin of modification or addition of potential in mechanics. A possible framework for the MOND theory and the dark matter
Frédéric Pierret
Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or…
Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus
Frédéric Pierret, Delfim F. M. Torres
We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentia…
Multiscale functions, Scale dynamics and Applications to partial differential equations
Jacky Cresson, Frédéric Pierret
Modeling phenomena from experimental data, always begin with a \emph{choice of hypothesis} on the observed dynamics such as \emph{determinism}, \emph{randomness}, \emph{derivabilit…
Helmholtz theorem for stochastic Hamiltonian systems
Frédéric Pierret
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamilton…
Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
Jacky Cresson, Frédéric Pierret
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inver…
Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations
Jacky Cresson, Frédéric Pierret
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of cat…
Coupling the non-gravitational forces and Modified Newton Dynamics for cometary orbits
Lucie Maquet, Frédéric Pierret
In recent work (Milgrom 2009, Blanchet & Novak 2011), the authors showed that MOdified Newton Dynamics (MOND) have a non-negligible secular perturbation effect on planets with larg…
A nonstandard Euler-Maruyama scheme
Frédéric Pierret
We construct a nonstandard finite difference numerical scheme to approximate stochastic differential equations (SDEs) using the idea of weighed step introduced by R.E. Mickens. We…
Non standard finite difference scheme preserving dynamical properties
Jacky Cresson, Frédéric Pierret
We study the construction of a non-standard finite differences numerical scheme for a general class of two dimensional differential equations including several models in population…
Helmholtz theorem for Hamiltonian systems on time scales
Frédéric Pierret
We derive the Helmholtz theorem for Hamiltonian systems defined on time scales in the context of nonshifted calculus of variations which encompass the discrete and continuous case.…
Dynamics of a rotating ellipsoid with a stochastic flattening
Etienne Behar, Jacky Cresson, Frédéric Pierret
Experimental data suggest that the Earth short time dynamics is related to stochastic fluctuation of its shape. As a first approach to this problem, we derive a toy-model for the m…
Stochastic Gauss Equations
Frédéric Pierret
We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit…
The Sharma-Parthasarathy stochastic two-body problem
Jacky Cresson, Frédéric Pierret, Bénédicte Puig
We study the Sharma-Parthasarathy stochastic two-body problem introduced by N. Sharma and H. Parthasarathy in \cite{sharma}. In particular, we focus on the preservation of some fun…