Related papers: Residual periodicity on the Markoff surface
Drawing the secant through two rational points of a cubic surface we can get the third one. Is the set of rational points finitely generated? We discuss some numerical data and prove a finite generation statement with respect to a modified…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Many natural and social systems possess power-law memory, and their mathematical modeling requires the application of discrete and continuous fractional calculus. Most of these systems are nonlinear and demonstrate regular and chaotic…
Let f be a transcendental map, and let U be an attracting or parabolic basin, or a doubly parabolic Baker domain. Assume U is simply connected. Then, we prove that periodic points are dense in the boundary of U, under certain hypothesis on…
Piecewise smooth maps are known to exhibit a wide range of dynamical features including numerous types of periodic orbits. Predicting regions in parameter space where such periodic orbits might occur and determining their stability is…
Dynamical systems on an infinite translation surface with the lattice property are studied. The geodesic flow on this surface is found to be recurrent in all but countably many rational directions. Hyperbolic elements of the affine…
Let $\phi$ be a an endomorphism of degree $d\geq{2}$ of the projective line, defined over a number field $K$. Let $S$ be a finite set of places of $K$, including the archimedean places, such that $\phi$ has good reduction outside of $S$.…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We consider the viscous incompressible fluids in a three-dimensional horizontally periodic domain bounded below by a fixed smooth boundary and above by a free moving surface. The fluid dynamics are governed by the Navier-Stokes equations…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
Given a quadratic polynomial with rational coefficients, we investigate the existence of consecutive squares in the orbit of a rational point under the iteration of the polynomial. We display three different constructions of $1$-parameter…
We study time-like surfaces in the three-dimensional Minkowski space with diagonalizable second fundamental form. On any time-like W-surface we introduce locally natural principal parameters and prove that such a surface is determined…
A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…
Fix a rational basepoint b and a rational number c. For the quadratic dynamical system f_c(x) = x^2+c, it has been shown that the number of rational points in the backward orbit of b is bounded independent of the choice of rational…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete,…
We show that S. Saito's fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a…
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycle with period at least two implies that the random rotation…
Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the…
Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion…