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11. 6. 2024.
Period-Two Trichotomies of a Difference Equation of Order Higher Than Two
We investigate the period-two trichotomies of solutions of the equation $$x_{n+1} = f(x_{n}, x_{n-1},x_{n-2}), \quad n=0, 1, \ldots $$ where the function $f$ satisfies certain monotonicity conditions. We give fairly general conditions for period-two trichotomies to occur and illustrate the results with numerous examples. 1991 Mathematics Subject Classification. 39A10, 39A11