On number of interior periodic points of a Lotka-Volterra map (Q2889712)

In this article, the author gives a lower estimate of the number of periodic points of period interiors \( n \leq \) 36 to the application NEWLINE\[NEWLINEF:\Delta \rightarrow \Delta\quad F(x,y)=(x(4-x-y),xy),NEWLINE\]NEWLINE where \(\Delta =\{(x,y)\in \mathbb{R}^2/0\leq x,\;0\leq y,\;x+y\leq 4\}\). This application \( F \) was proposed by Sharkovskii in 1993 and is sometimes referred to as the discrete Lotka-Volterra map.NEWLINENEWLINEThe idea is to use the results of the author [J. Difference Equ. Appl. 18, No. 4, 553--567 (2012; Zbl 1246.37063)] that put in correspondence interior periodic points with saddle lower boundary periodic points. The dynamics on this lower boundary is the logistic map \( x \rightarrow x (4-x) \), and saddle points of the two-dimensional system correspond to points in the one-dimensional system that are completely unstable points. The result thus obtained calculates the number of completely unstable periodic points of the logistic map. The author also includes results in order to reduce the number of calculations needed in this computation.