we investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  in particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

There exist gravitational memory effects in Brans-Dicke theory. They are closely related to the Bondi-Metzner-Sachs symmetries living on null infinity an isolated system. By studying asymptotically flat spacetime theory and asymptotic symmetries, one discovers that displacement effect tensor sector is due vacuum transition caused by energy fluxes panetrating infinity, while scalar sector, angul...

Numerous numerical studies indicate that dark matter halos show an almost universal radial density profile. The origin of the profile is still under debate. We investigate this topic and pay particular attention to the velocity dispersion profile. To this end we have performed high-resolution simulations with two independent codes, ART and Gadget. The radial velocity dispersion can be approxima...

For a group G, we denote by G↔ the coarse space on G endowed with structure base {{(x,y)∈G×G:y∈xF}:F∈[G]<ω}, xF={z−1xz:z∈F}. Our goal is to explore interplays between algebraic properties of and asymptotic G↔. In particular, show that asdim G↔=0 if only G/ZG locally finite, ZG center G. an infinite subgroups discrete Dedekind group.

Asymptotic regimes of geophysical dynamics are described for di erent Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit of strong strati cation in the Burger number of order one situation as well as in the asymptotic regime of strong strati cation and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic in...

In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine parametric conditions for local asymptotic stability of fixed points model. Furthermore, with use center manifold theorem and bifurcation theory, we analyze existence directions period-doubling Neimark-Sacker bifurcations. The plots maximum Lyapunov exponents provide indications complexity chao...

The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossin...

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The effective response of a periodic fibre reinforced material to SH wave propagation is studied using the method of asymptotic homogenization, complex variable theory and multipole expansions. The quasi-static limit of the effective properties is calculated when the wavelength is much longer than the defining lengthscale of the microstructure. The method developed allows the determination of t...

Abstract. When a spacetime takes Bondi radiating metric, and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy-momentum is the past limit of the Bondi energy-momentum. We also derive a formula relating the ADM energy-momentum of any asymptotically flat spacelike hypersurface to the Bondi energy-momentum of any nu...