Related papers: Fiberwise Convexity of Hill's lunar problem

We investigate the dynamics of a two-degree-of-freedom mechanical system for energies slightly above a critical value. The critical set of the potential function is assumed to contain a finite number of saddle points. As the energy…

We consider the planar Hill's lunar problem with a homogeneous gravitational potential. The investigation of the system is twofold. First, the starting conditions of the trajectories are classified into three classes, that is bounded,…

The perturbation of the lunar motion caused by a hypothetical violation of the equivalence principle is analytically worked out in terms of power series \`a la Hill-Brown. The interaction with the quadrupolar tide is found to amplify the…

We investigate the Cartan and Finsler geometry of the rotating Kepler problem, a limit case of the restricted three body problem that arises if the mass of the one of the primaries goes to zero. We show that the Hamiltonian for the rotating…

The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using…

A trivial projective change of a Finsler metric $F$ is the Finsler metric $F + df$. I explain when it is possible to make a given Finsler metric both forward and backward complete by a trivial projective change. The problem actually came…

The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…

For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The…

We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has…

Consider the steady neutron transport equation with diffusive boundary condition. In [Wu and Guo(2015) Comm. Math. Phys.] and [Wu and Yang and Guo(2016) Preprint], it was discovered that geometric correction is necessary for the Milne…

For the axisymmetric incompressible Euler equations, we prove linear in time filamentation near Hill's vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining the recent…

The Hubble constant proves to be the pseudo-Finsleroid--Landsberg factor. The covariantly conserved pseudo-Finsleroid--gravitational tensor is explicitly found after evaluating the respective Finsleroid--case curvature tensor and required…

In this paper, I mainly prove the following results. For every energy value below the minimum of the first, second and third critical value, each bounded component of the regularized energy hypersurface of the Lagrange problem under some…

The goal of this short paper is to give condition for the completeness of the Binet-Legendre metric in Finsler geometry. The case of the Funk and Hilbert metrics in a convex domain are discussed.

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…

In this paper we fully characterize the sequentially weakly lower semicontinuity of the parameter-depending energy functional associated with the critical Kirchhoff problem. We also establish sufficient criteria with respect to the…

Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The results are generalized to include period variations from cycle to…

We examine perturbatively the two-Higgs-doublet extension of the \SM\ in the context of the suspected triviality of theories with fundamental scalars. Requiring the model to define a consistent effective theory for scales below a cutoff of…

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In…

We derive the geodesic equation for relatively K\"ahler metrics on fibrations and prove that any two such metrics with fibrewise constant scalar curvature are joined by a unique smooth geodesic. We then show convexity of the log-norm…