Linear Fractional Recurrences: Periodicities and Integrability
نویسندگان
چکیده
منابع مشابه
Se p 20 05 Periodicities in Linear Fractional Recurrences : Degree growth of birational surface maps
A natural question is: for what values of α and β can (0.1) generate a periodic recurrence? In other words, when does (0.1) generate a periodic sequence (xn) for all choices of x1, . . . , xp? This is equivalent to asking when there is an N such that f α,β is the identity map. Periodicities in recurrences of the form (0.1) have been studied in [L, KG, KoL, GL, CL]. The question of determining t...
متن کاملIntegrability and non-integrability of periodic non-autonomous Lyness recurrences∗
This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an +xn+1)/xn, where {an} is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k ∈ {1, 2, 3, 6} the behavior of the sequence {xn} is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases ...
متن کاملDiophantine Equations Related with Linear Binary Recurrences
In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...
متن کاملLinear Recurrences and Chebyshev Polynomials
with given a, b, t0, t1 and n ≥ 0. This sequence was introduced by Horadam [3] in 1965, and it generalizes many sequences (see [1, 4]). Examples of such sequences are Fibonacci polynomials sequence (Fn(x))n≥0, Lucas polynomials sequence (Ln(x))n≥0, and Pell polynomials sequence (Pn(x))n≥0, when one has a = x, b = t1 = 1, t0 = 0; a = t1 = x, b = 1, t0 = 2; and a = 2x, b = t1 = 1, t0 = 0; respect...
متن کاملCirculants , Linear Recurrences and Codes
We shall give some intriguing applications of the theory of circulants—the circulant matrices—and that of linear recurrence sequences (LRS). The applications of the former in §2 ranges from a simple derivation of the Blahut theorem to the energy levels of hydrogen atoms in circular hydrocarbons, where the Blahut theorem is to the effect that the Hamming weight of a code is equal to the rank of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2011
ISSN: 0240-2963
DOI: 10.5802/afst.1304