A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New orbits found in Lagrangian systems on surfaces.
Global minimizers exist for Tonelli Lagrangians on half-Lie groups.
New curvature measure for optimal transport with specific cost function.
The study finds infinitely many periodic orbits just above a critical value on a 2-sphere.
We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $T^*\T^n$ of the -dimensional torus that have no conjugate points are integrable, i.e. $T^*\T^n$ is foliated by a family $\Fc$ of invariant Lagrangian graphs. Assuming that the Hamiltonian is , we prove that there …
In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type , where is the Riemannian distance of a complete …
An example from Almgren and Federer shows geodesics that are not always the shortest.
Variational reduction simplifies Lagrangian systems with scaling symmetries.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
New Lagrangians found by modifying existing ones.
Paper finds periodic orbits for convex Lagrangian systems on noncompact manifolds.
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new Lagrangian in an extended configuration space ---which we call D'Alambert's--- com…
Bayesian framework discovers interpretable Lagrangian from data.
Visible Lagrangians in Hitchin systems are studied for pillowcase covers.
Automates discovery of interpretable Lagrangians from data.
Alternative approach to regularize time-dependent singular Lagrangian systems.
Derives equations for forced systems using variational methods.
The paper studies bifurcations in Lagrangian systems and geodesics.
New method fills cluster seeds with exact Lagrangian structures.
A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the ca…
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
Researchers find a method to represent bi-Hamiltonian systems using Lagrangian representations.
Survey of Lagrangian reduction for discrete mechanical systems.
Geodesic extensions for systems with nonholonomic constraints.
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangi…
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
The classes of Monge-Ampère systems, decomposable and bi-decomposable Monge-Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based on the existence of …
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its usual interpretation can not be applied to homogeneous Lagrangians found in relativi…
New variational principles found for conformal geodesics.
This paper extends the evolution operator to contact mechanics, linking Lagrangian and Hamiltonian formulations.
The paper simplifies complex mechanical systems with external forces.
We illustrate the theory of one-dimensional pluri-Lagrangian systems with the example of commuting billiard maps in confocal quadrics.
In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.
New Lagrangian approach for optimal control of second-order systems.
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manif…
We construct singular solutions to special Lagrangian equa- tions with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced cor- respondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.
New approach to Lagrangian systems using intrinsic geometry.
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed …
The differential system for minimal Lagrangian surfaces in a -dimensional, non-flat, complex space form is an elliptic system defined on the bundle of oriented Lagrangian planes. This is a 6-symmetric space associated with the Lie group SL(3,), and the minimal Lagrangian surfaces arise as th…
This is the sixth in a series of papers constructing examples of special Lagrangian m-folds in C^m. We present a construction of special Lagrangian cones in C^3 involving two commuting o.d.e.s, motivated by the first two papers of the series. Then we generalize it to a construction of non-conical special Lagrangian 3-f…
Model learns Lagrangian dynamics from images for better prediction and control.
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noe…
The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the energy of the Lagrange space and the external force field. We study the variation of the energy and Lagrangian functions along the evolution and…
Functor connects sheaves on Lagrangian cobordisms, proving equivalence and action decreasing properties.
We study Hamiltonian stationary Lagrangian surfaces in C^2, i.e. Lagrangian surfaces in C^2 which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representatio…
In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian pa…
Researchers develop neural optimal transport with Lagrangian costs for efficient computation.
Motivated by various results on homogeneous geodesics of Riemannian spaces, we study homogeneous trajectories, i.e. trajectories which are orbits of a one-parameter symmetry group, of Lagrangian and Hamiltonian systems. We present criteria under which an orbit of a one-parameter subgroup of a symmetry group G is a solu…