Related papers: Maxwell Strata in the sub-Riemannian problem on so…

In the present article the geometry of semi-Riemannian manifolds with nonholonomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where the positively definite metric is substituted…

We propose a generalization of two classes of Lie-Hamilton systems on the Euclidean plane to two-dimensional curved spaces, leading to novel Lie-Hamilton systems on Riemannian spaces (flat $2$-torus, product of hyperbolic lines, sphere and…

This article carries out the investigation of a three-dimensional Riemannian manifold $N^3$ endowed with a semi-symmetric type non-metric connection. Firstly, we construct a non-trivial example to prove the existence of a semi-symmetric…

In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a…

The contraction of the Poincare group with respect to the space trans- lations subgroup gives rise to a group that bears a certain duality relation to the Galilei group, that is, the contraction limit of the Poincare group with respect to…

A dynamical Maxwell system is \begin{align*} & e_t={\rm curl\,} h, \quad h_t=-{\rm curl\,} e &&{\rm in}\,\,\Omega \times (0,T) & e|_{t=0}=0,\,\,\,\,h|_{t=0}=0 &&{\rm in}\,\,\Omega & e_\theta =f &&{\rm in}\,\,\, \partial\Omega \times [0,T]…

Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…

We explicitly describe the length minimizing geodesics for a sub-Riemannian structure of the elliptic type defined on $SL(2, \mathbb{R})$. Our method uses a symmetry reduction which translates the problem into a Riemannian problem on a two…

Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of the nonlinear Klein-Gordon-Maxwell system and nonlinear Schroedinger-Maxwell system with subcritical nonlinearity. We prove that the…

We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain of $\mathbb{R}^{3}$ with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate…

Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…

The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. The question of existence of an optimal solution is nontrivial…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

The main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent Hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating…

The Hamiltonian analysis for a 3-dimensional connection dynamics of $\frak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01}, L_{02}, L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the…

In this article, we study the following Hamiltonian system: \begin{equation*} \begin{cases} \begin{aligned} &-\varepsilon^{2}\Delta_{g} u +u = |v|^{q-1}v, &-\varepsilon^{2}\Delta_{g} v +v = |u|^{p-1}u && \text{ in } \mathcal{M}, & \quad u,v…

The Hamiltonian approach to isomonodromic deformation systems is extended to include generic rational covariant derivative operators on the Riemann sphere with irregular singularities of arbitrary Poincar\'e rank. The space of rational…

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg…

We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus,…

We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of…