Related papers: The meromorphic non-integrability of the planar th…
We give results on the following questions about a topologically tame hyperbolic 3-manifold M : 1. Does M have nonzero square-integrable harmonic 1-forms? 2. Does zero lie in the spectrum of the Laplacian acting on (1-forms on M)/Ker(d)?
We consider third order Lovelock gravity coupled to an U(1) gauge field for which its Lagrangian is given by a power of Maxwell invariant. In this paper, we present a class of horizon flat rotating black branes and investigate their…
The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \& Ehlers 1993) is evaluated up to the third order. On its basis a model for…
The aim of the present work is to extend the a priori error for contact problems with an augmented Lagrangian method. We focus on unilateral contact problem without friction between an elastic body and a rigid one. We consider the…
In this paper we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations with entire or meromorphic coefficients. We further extend and improve few results on the order of meromorphic…
Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…
In this work, we present a new approach to the construction of variational integrators. In the general case, the estimation of the action integral in a time interval $[q_k,q_{k+1}]$ is used to construct a symplectic map $(q_k,q_{k+1})\to…
In this paper, an approach is developed to solve the three body problem involving masses which posses spherical symmetry. The problem dates back to the times of Poincare, and is undoubtedly one of the oldest of unsolved problems of…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many…
We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with a rigid inclusion. Our analysis is based on the boundary integral formulation of the elastostatic problem and geometric function…
The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the…
Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…
We carry out a sequence of coordinate changes for the planar three-body problem which successively eliminate the translation and rotation symmetries, regularize all three double collision singularities and blow-up the triple collision.…
We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time,we…
Let $\mathcal{F}$ be a foliation defined on a complex projective manifold $M$ of dimension $n$ and admitting a holomorphic vector field $X$ tangent to it along some non-empty Zariski-open set. In this paper we prove that if $X$ has…
We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted…
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable…
We observe that a particular first integral of the partially-averaged system in the secular theory of the three-body problem appears also as an important conserved quantity of integrable Kepler billiards. In this note we illustrate their…