Related papers: Fixed points and the inverse problem for central c…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
In this present article, we get sufficient conditions for the existence and uniqueness of fixed points and common fixed points for single and double mapping satisfying various contractive conditions within the partially ordered…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…
The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a…
We discuss several conditions for four points to lie on a plane, and we use them to find new equations for four-body central configurations that use angles as variables. We use these equations to give novel proofs of some results for…
For the planar $N$-body problem, we first introduce a class of moving frame suitable for orbits near central configurations, especially for total collision orbits, which is the main new ingredient of this paper. The moving frame allows us…
In this work, we introduce the concept of $C^{*}$-algebra valued asymetric metric space, the concept of forward and the concept of backward $C^{*}$ valued asymetric contractions. We discuss the existence and uniqueness of fixed points for a…
In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.
Quantum systems in extreme conditions can exhibit universal behavior far from equilibrium associated to nonthermal fixed points with a wide range of topical applications from early-universe inflaton dynamics and heavy-ion collisions to…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
This paper examines the existence of centered co-circular central configurations in the general power-law potential n-body problem. We prove the nonexistence of such configurations when the system consists of n-3 equal masses and three…
We study the fixed point sets of holomorphic self-maps of a bounded domain in ${\Bbb C}^n$. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be…
In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the…
In this study, we present a rigorous analytical proof of the uniqueness of central configurations for the five-body problem, assuming that all five masses are equal and positioned at the vertices of a planar polygon. We consider…