Zobrazeno 1 - 10
of 44
pro vyhledávání: '"Pierret, Frédéric"'
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 internal. The rst case corresponds to add a noise term to a given equa
Externí odkaz:
http://arxiv.org/abs/1812.06634
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 well as the discrete one and corrects a previous statement of Bartosiewi
Externí odkaz:
http://arxiv.org/abs/1609.02698
Publikováno v:
Discrete Dyn. Nat. Soc. 2016 (2016), Art. ID 8073023, 8 pp
We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation. Moreover, in the a
Externí odkaz:
http://arxiv.org/abs/1601.02602
Autor:
Pierret, Frédéric
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 modifying potentials in mechanics and specifically in galactic dynami
Externí odkaz:
http://arxiv.org/abs/1601.01130
Autor:
Cresson, Jacky, Pierret, Frédéric
Modeling phenomena from experimental data, always begin with a \emph{choice of hypothesis} on the observed dynamics such as \emph{determinism}, \emph{randomness}, \emph{derivability} etc. Depending on these choices, different behaviors can be observe
Externí odkaz:
http://arxiv.org/abs/1509.01048
Autor:
Pierret, Frédéric
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associ
Externí odkaz:
http://arxiv.org/abs/1507.06193
Autor:
Cresson, Jacky, Pierret, Frédéric
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 inverse problem for the discrete calculus of variation in the Hamiltonian s
Externí odkaz:
http://arxiv.org/abs/1501.03203
Autor:
Cresson, Jacky, Pierret, Frédéric
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 category theory. For ordinary differential equations we exhibit three mai
Externí odkaz:
http://arxiv.org/abs/1411.7117
Autor:
Maquet, Lucie, Pierret, Frédéric
Publikováno v:
Phys. Rev. D 91, 084015 (2015)
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 large semi-major axes (gaseous planets) in the Solar System. Some comets a
Externí odkaz:
http://arxiv.org/abs/1411.6146
Autor:
Pierret, Frédéric
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 prove the strong convergence of our scheme under locally Lipschitz con
Externí odkaz:
http://arxiv.org/abs/1411.2220