The space of new Generalized functions ζ (Π(R)) has been constructed. The operation of associative multiplication Θ has been defined on ζ (Π(R)).The embedding J_π : ζ(S(R))→ ζ( (R)) has been constructed

We introduce a recursive sequence with a piecewise defined function as the right hand side. This function is discontinuous and includes nonlinear terms, i.e. one branch of this function contains an integer exponent. We present results concerning the asymptotic behavior of the sequence. We specify conditions under which the sequence becomes a monotone divergent sequence. On the other hand we specify conditions under which the sequence converges to a fixed point or a finite cycle. We make a partial bifurcation analysis for the behavior of the sequence by fixing one parameter. Also, in this analsysis we considered just one start value for the sequence.

No abstract

Abstract:The space of new generalized functions has been constructed. The operation of associative multiplication has been defined on this space. The Extended Laplace Transform has been defined.

In this paper, we consider the explicit solution of the following system of nonlinear rational difference equations: x n + 1 = x n - 1 / x n - 1 + r , y n + 1 = x n - 1 y n / x n - 1 y n + r , with initial conditions x - 1 , x 0 and y 0 , which are arbitrary positive real numbers. By doing this, we encounter the hypergeometric function. We also investigate global dynamics of this system. The global dynamics of this system consists of two kind of bifurcations.