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In this work, we investigate the inverse problem of determining a quasilinear term appearing in a nonlinear elliptic equation from the measurement of the conormal derivative on the boundary. This problem arises in several practical…
We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial…
In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the…
The stability issue of generalized modified gravitational models is discussed with particular emphasis to de Sitter solutions. Two approaches are briefly presented.
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
We study the linear stability of $(1+n)$-gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the $(1+n)$-gon central configurations. We show that for $n\geq 8$ and any eccentricity $e\in[0,1)$,…
In this paper, we propose a distributed computing approach to solving large-scale robust stability problems on the simplex. Our approach is to formulate the robust stability problem as an optimization problem with polynomial variables and…
In this paper we investigate gravitationally bound, spherically symmetric equilibrium configurations consisting of ordinary (polytropic) matter nonminimally coupled to an external chameleon scalar field. We show that this system has static,…
In this paper we discuss about the possibility of {\it coexistence} of stable and unstable quasi--periodic {\sc kam} tori in a region of phase space of the three-body problem. The {argument of proof} goes along {{\sc kam} theory and,…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
In this paper, the linear stability theory of an incompressible asymptotic suction boundary layer was studied. A small disturbance was introduced spatially in a streamwise direction to the laminar base flow with various wavenumber $\alpha =…
In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…
We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems…
The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
We investigate the stability regions of hypothetical terrestrial planets around the Lagrangian equilibrium points L4 and L5 in some specific extrasolar planetary systems. The problem of their stability can be treated in the framework of the…
The notion of a weak stability boundary has been successfully used to design low energy trajectories from the Earth to the Moon. The structure of this boundary has been investigated in a number of studies, where partial results have been…
The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…