Related papers: Majorant series for the $N$-body problem
We show the existence of some infinite families of periodic solutions of the planar Newtonian n-body problem --with positive masses-- which are symmetric with respect to suitable actions of finite groups (under a strong--force assumption,…
Within the framework of teleparallel equivalent of general relativity (TEGR) theory, calculation of the total energy and momentum of Kerr-NUT spacetimes have been employed using two methods of the gravitational energy-momentum, which is…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
We construct majorant functions $\Phi (t,z)$ for the Mayer series of pressure satisfying a nonlinear differential equation of first order which can be solved by the method of characteristics. The domain $| z| <(e\tau) ^{-1}$ of convergence…
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…
We describe a new method of calculating the renormalised energy of a field obeying the Maxwell and Dirac equations. The method does not involve evaluating integrals but relies instead on summing a geometric series. We show that the new…
We construct an evolution equation for the $B$ meson wave functions in the $k_T$ factorization theorem, whose solutions sum the double logarithms associated with the light-cone singularities, namely, the rapidity logarithms. The derivation…
We re-examine the series of resonances found earlier in atomic three-body systems by solving the Faddeev-Merkuriev integral equations. These resonances are rather broad and line-up at each threshold with gradually increasing gaps, the same…
The non-perturbative {\it ab initio} calculations of infinite nuclear matter using In-Medium Similarity Renormalization Group (IMSRG) method is developed in this work, which enables calculations with chiral two and three-nucleon forces at…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
In a companion paper arXiv:2510.27676, we introduced a non-perturbative classical renormalisation group (RG) flow equation as a novel method for treating strongly interacting problems in general relativity, with a prominent application to…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…
We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy…
Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration…
We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the…
We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mandelbrojt and becomes useful and necessary when working with…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…