Periodicity and convergence for xn+1=|xn−xn−1|

Periodicity and convergence for xn + 1 = | xn − xn − 1 |

Each solution {xn} of the equation in the title is either eventually periodic with period 3 or else, it converges to zero—which case occurs depends on whether the ratio of the initial values of {xn} is rational or irrational. Further, the sequence of ratios {xn/xn−1} satisfies a first-order difference equation that has periodic orbits of all integer periods except 3. p-cycles for each p = 3 are...

Periodicity and Almost-periodicity

Convergence and Periodicity of Solutions for a Class of Difference Systems

A class of difference systems of artificial neural network with two neurons is considered. Using iterative technique, the sufficient conditions for convergence and periodicity of solutions are obtained in several cases.

Periodicity and Quasi-periodicity for Super-integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single-valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a com-mensurability condition is imposed on an angular momentum component. R ´ ESUMÉ...

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...