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The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
This study investigates the problem of areostationary orbits around Mars in the three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no…
On a basis of theory of Riemann extension of the space of constant affine connection associated with the R\"ossler system of equations relations between its parameters are investigated.
General area-preserving motion of polygonal curves is formulated as a system of ODEs. Solution polygonal curves belong to a prescribed polygonal class, which is similar to the admissible class used in the crystalline curvature flow. The…
The paper discusses the conditions for the existence of fixed points of multivalued mappings that are not based on the linear structure of the set. The descriptions for the sets of fixed points for mappings with closed graph in compact…
The main goal of this paper is to present orbital stability results of periodic standing waves for the one-dimensional logarithmic Klein-Gordon equation. To do so, we first use compactness arguments and a non-standard analysis to obtain the…
In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we…
We show that if the rotation set of a homeomorphism of the torus is stable under small perturbations of the dynamics, then it is a convex polygon with rational vertices. We also show that such homeomorphisms are $C^0$-generic and have…
We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
This paper is largely concerned with constructing coarse moduli spaces for Artin stacks. The main purpose of this paper is to introduce the notion of stability on an arbitrary Artin stack and construct a coarse moduli space for the open…
Stable quotient spaces provide an alternative to stable maps for compactifying spaces of maps. When the target is projective space and the domain curve has genus 1, these are smooth proper Deligne-Mumford stacks. In this paper we study the…
The image of the Gauss map of any oriented isoparametric hypersurface of the unit standard sphere $S^{n+1}(1)$ is a minimal Lagrangian submanifold in the complex hyperquadric $Q_n({\mathbf C})$. In this paper we show that the Gauss image of…
We propose the concepts of vicinal mappings and firmly vicinal mappings in metric spaces. We obtain fixed point and convergence theorems for these mappings in complete geodesic spaces with curvature bounded above by one and apply our…
(Abridged) We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly concentrate on the study of the HD 82943 system by employing two sets of the…
Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $\lambda$, we study Hyers-Ulam stability of the global differential equation $Vy=\lambda…
We consider convex maps f:R^n -> R^n that are monotone (i.e., that preserve the product ordering of R^n), and nonexpansive for the sup-norm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the…