The notion of almost periodicity nontrivially generalizes the notion of periodicity. Strongly almost periodic sequences (=uniformly recurrent infinite words) first appeared in the field of symbolic dynamics, but then turned out to be interesting in connection with computer science. The paper studies the class of eventually strongly almost periodic sequences (i. e., becoming strongly almost peri...

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.

In this research work, let’s focus on the construction of numerical scheme based radial basis functions finite difference (RBF-FD) method combined with Laplace transform for solution fractional order dispersive wave equations. The is then applied to examine eventual periodicity proposed model subject periodic boundary conditions. implementation technique high and integer type nonlinear partial ...

Studied here is the large-time behavior and eventual periodicity of solutions of initial-boundary-value problems for the BBM equation and the KdV equation, with and without a Burgers-type dissipation appended. It is shown that the total energy of a solution of these problems grows at an algebraic rate which is in fact sharp for solutions of the associated linear equations. We also establish tha...

Piecewise-isometries are zero-entropy dynamical systems with very complex behaviour. In one-dimension they are intervalexchange transformations (IET), which are connected to diophantine arithmetic by the Boshernitzan and Carrol theorem: in any IET defined over a quadratic number field, the process of induction results, after scaling, in an eventually periodic sequence of IETs. This can be viewe...

Convergence results are presented for rank-type difference equations, whose evolution rule is defined at each step as the kth largest of p univariate difference equations. If the univariate equations are individually contractive, then the equation converges to a fixed point equal to the kth largest of the individual fixed points of the univariate equations. Examples are max-type equations for k...