Related papers: Jacobi structure for dissipative mechanical system…

We study affine Jacobi structures on an affine bundle $\pi:A\to M$, i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between affine Jacobi structures on $A$ and Lie algebroid structures…

We prove the existence of a local analytic Levi decomposition for analytic Poisson structures and Lie algebroids.

A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to…

We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups. Also, we find some examples of Jacobi-Lie Hamiltonian…

We define compatibility between Jacobi structures and pseudo-Riemannian cometrics on Jacobi algebroids. This notion is a generalization of the compatibility between Poisson structures and pseudo-Riemannian cometrics on manifolds, which was…

We review nonabelian Poisson structures on affine and projective spaces over $\mathbb{C}$. We also construct a class of examples of nonabelian Poisson structures on $\mathbb{C} P^{n-1}$ for $n>2$. These nonabelian Poisson structures depend…

A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…

Using the concept of Jacobi-Lie group and Jacobi-Lie bialgebra, we generalize the definition of Poisson-Lie symmetry to Jacobi-Lie symmetry. In this regard, we generalize the concept of Poisson-Lie T-duality to Jacobi-Lie T-duality and…

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…

In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear naturally when applying reciprocal transformations to Hamiltonian…

New generalized Poisson structures are introduced by using skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are given by the vanishing of the Schouten-Nijenhuis bracket. As an example, we provide the…

In this paper, we present a relation between Jacobi-Reeb dynamics and the dynamics associated with a mechanical Hamiltonian system with respect to a linear Poisson structure on a vector bundle. For this purpose, we will use the so-called…

Classical mechanical systems are defined by their kinetic and potential energies. They generate a Lie algebra under the canonical Poisson bracket. This Lie algebra, which is usually infinite dimensional, is useful in analyzing the system,…

Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra $A$ and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for…

We define Dirac pairs on Jacobi algebroids, which is a generalization of Dirac pairs on Lie algebroids introduced by Kosmann-Schwarzbach. We show the relationship between Dirac pairs on Lie and on Jacobi algebroids, and that Dirac pairs on…

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several…

In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even…

We show that the space of observables of test particles carries a natural Jacobi structure which is manifestly invariant under the action of the Poincar\'{e} group. Poisson algebras may be obtained by imposing further requirements. A…

The idea of dissipative mechanical system with delay is proposed. The paper studies the phenomenon of dissipation with delay for Euler-Poincare systems on Lie algebras or equivalently, for Lie-Poisson systems on the duals of Lie algebras.…

We describe a method for solving the Maurer-Cartan structure equation associated with a Lie algebra that isolates the role of the Jacobi identity as an obstruction to integration. We show that the method naturally adapts to two other…