منابع مشابه
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...
متن کاملON BOUNDEDNESS OF THE SOLUTIONS OF THE DIFFERENCE EQUATION xn+1=xn-1/(p+xn)
Theorem 1. (i) If p > 1, then the unique equilibrium 0 of (1) is globally asymptotically stable. (ii) If p = 1, then every positive solution of (1) converges to a period-two solution. (iii) If 0 < p < 1, then 0 and x = 1− p are the only equilibrium points of (1), and every positive solution {xn}n=−1 of (1) with (xN − x)(xN+1 − x) < 0 for some N ≥ −1 is unbounded. They proposed the following ope...
متن کاملOn the Burnside Semigroups xn = xn+m
In this paper we prove that the congruence classes of A associated to the Burnside semigroup with jAj generators deened by the equation x n = x n+m , for n 4 and m 1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m = 1 and n 2. De Luca and Varricchio solved the problem for n 5 in 90. A little later, McCammond extended the problem for m 1 and solved it indepe...
متن کاملGlobal Behavior of the Max-Type Difference Equation xn+1=max{1/xn,An/xn-1}
and Applied Analysis 3 Lemma 2.5. Let {xn}n −1 be a positive solution of 1.1 and limn→∞Pn S. Then S lim supn→∞xn. Proof. Since Pn is a subsequence of xn, it follows that S ≤ lim sup n→∞ xn. 2.6 On the other hand, by xn 1 ≤ Pn for all n ≥ 1, we obtain lim sup n→∞ xn ≤ lim sup n→∞ Pn S. 2.7 The proof is complete. Remark 2.6. Let {xn}n −1 be a positive solution of 1.1 . By Lemma 2.2, we see that i...
متن کاملOn the Max-Type Difference Equation xn+1=max{A/xn,xn-3}
The study of max-type difference equations attracted recently a considerable attention, see, for example, 1–27 , and the references listed therein. This type of difference equations stems from, for example, certain models in automatic control theory see 28 . In the beginning of the study of these equations experts have been focused on the investigation of the behavior of some particular cases o...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1977
ISSN: 0021-8693
DOI: 10.1016/0021-8693(77)90291-5