Related papers: Affine Hamiltonians in higher order geometry

By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…

We study several aspects of the regular deformations of completely integrable systems. Namely, we prove the existence of a Hamiltonian normal form for these deformations and we show the necessary and sufficient conditions a perturbation has…

Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of…

This paper has been inspired by ideas presented by V. V. Kozlov in his works [19, 20]. In this paper our goal is to carry out a thorough analysis of some geometric problems of the dynamics of affinely-rigid bodies. We present two ways to…

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those…

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow…

Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $\Lambda$, is reexpressed as an affine algebra with the commutator of the imaginary part of the…

Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in…

A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative…

We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a…

We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples, including recently found…

In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (\rho,\eta)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented.…

We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials…

We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of the displacement group, the other one by a property of the…

An inifinite-dimensional representation of the double affine Hecke algebra of rank 1 and type $(C_1^{\vee},C_1)$ in which all generators are tridiagonal is presented. This representation naturally leads to two systems of polynomials that…

In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity…

We study affine Grassmannians for ramified triality groups. These groups are of type ${}^3D_4$, so they are forms of the orthogonal or the spin groups in 8 variables. They can be given as automorphisms of certain twisted composition…