We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

*Correspondence: [email protected] 2Department of Mathematics, Yanbian University, Yanji, 133002, P.R. China Full list of author information is available at the end of the article Abstract In this paper, the concepts of a right fractional sum and right fractional difference operators are introduced. Some basic properties of a right fractional sum and right fractional difference operators are pr...

The paper gives recurrence relations on the number of 2n step fully extended (i.e., full-dimensional) self-avoiding polygons in n-and (n-1)-dimensional integer lattices.

In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation ut = (K(u)ux)x+Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes the paper [J. Phys. A: Math. Gen. 30, Nr. 23 (1997), 8139–8155], where a few invariant models for he...