Related papers: On generalized nonholonomic Chaplygin sphere probl…

We consider a Cauchy Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the…

We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…

We prove two new results about the Cauchy problem for nonlinear Schroedinger equations on four-dimensional compact manifolds. The first one concerns global wellposedness for Hartree-type nonlinearities and includes approximations of cubic…

The purpose of this paper is to study the properties of holomorphic Poisson manifolds $(M,\pi)$ under the assumption of $\partial_{}\bar{\partial}$--lemma or $\partial_{\pi}\bar{\partial}$--lemma. Under these assumptions,we show that the…

In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions…

The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the…

We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of…

For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions…

The aim of this comment is to call to the attention of DSR readers a basic fact. The introduction of noncommutative structures in problems like the one addressed in [1] is not necessary for the understanding of DSR physics. It can be…

Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in ${\mathbb R}^3$ is proposed. Compatible Poisson structures and the corresponding bi-Hamiltonian N=3 systems are also…

We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…

The Neumann and Chaplygin systems on the sphere are simultaneously separable in variables obtained from the standard elliptic coordinates by the proper Backlund transformation. We also prove that after similar Backlund transformations other…

Generalizing ideas of MacKay, and MacKay and Saffman, a necessary condition for the presence of high-frequency ( i.e., not modulational) instabilities of small-amplitude periodic solutions of Hamiltonian partial differential equations is…

This paper is concerned with the Chaplygin sleigh with timevarying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material point that executes periodic oscillations in a direction…

We prove the existence of a deformation quantization for integrable Poisson structures on R^3 and give a generalization for a special class of three dimensional manifolds.

We investigate a one-dimensional nonlinear wave system which arises from a variational principle modeling a type of cholesteric liquid crystals. The problem treated here is the Cauchy problem for the same wave speed case with initial data…

We give a detailed and improved presentation of our recently proposed formalism for non-linear perturbations in cosmology, based on a covariant and fully non-perturbative approach. We work, in particular, with a covector combining the…

We consider a curved space-time whose algebra of functions is the commutative limit of a noncommutative algebra and which has therefore an induced Poisson structure. In a simple example we determine a relation between this structure and the…

Using the wave equation in d > or = 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincar\'e and Galileo covariant with respect to different sets of independent variables. This provides a method to…

In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group…