60,261 research outputs found
Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
In this article, we present a brief overview of some of the recent progress
made in identifying and generating finite dimensional integrable nonlinear
dynamical systems, exhibiting interesting oscillatory and other solution
properties, including quantum aspects. Particularly we concentrate on Lienard
type nonlinear oscillators and their generalizations and coupled versions.
Specific systems include Mathews-Lakshmanan oscillators, modified Emden
equations, isochronous oscillators and generalizations. Nonstandard Lagrangian
and Hamiltonian formulations of some of these systems are also briefly touched
upon. Nonlocal transformations and linearization aspects are also discussed.Comment: To appear in Eur. Phys. J - ST 222, 665 (2013
Affine Weyl groups, discrete dynamical systems and Painleve equations
A new class of representations of affine Weyl groups on rational functions
are constructed, in order to formulate discrete dynamical systems associated
with affine root systems. As an application, some examples of difference and
differential systems of Painleve type are discussed.Comment: AMSLaTeX, 16 page
Galois differential algebras and categorical discretization of dynamical systems
A categorical theory for the discretization of a large class of dynamical
systems with variable coefficients is proposed. It is based on the existence of
covariant functors between the Rota category of Galois differential algebras
and suitable categories of abstract dynamical systems. The integrable maps
obtained share with their continuous counterparts a large class of solutions
and, in the linear case, the Picard-Vessiot group.Comment: 19 pages (examples added
Mode-coupling theory and the fluctuation-dissipation theorem for nonlinear Langevin equations with multiplicative noise
In this letter, we develop a mode-coupling theory for a class of nonlinear
Langevin equations with multiplicative noise using a field theoretic formalism.
These equations are simplified models of realistic colloidal suspensions. We
prove that the derived equations are consistent with the
fluctuation-dissipation theorem. We also discuss the generalization of the
result given here to real fluids, and the possible description of supercooled
fluids in the aging regime. We demonstrate that the standard idealized
mode-coupling theory is not consistent with the FDT in a strict field theoretic
sense.Comment: 14 pages, to appear in J. Phys.
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