zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Global attractivity and convergence of a difference equation. (English) Zbl 1185.37025
The authors study the global behavior of the difference equation $$x_{n+1}= {\beta x_{n-k+1}+\gamma x_{n-2k+1}\over A+ Cx_{n-2k+1}},\qquad n\ge 0,$$ where $\beta$, $\gamma$, $A$, $C$ are positive constants and the initial conditions $x_{2k+1},\dots, x_1,x_0$, $k\ge 1$, are nonnegative. The case where $k= 1$ was studied by {\it M. R. S. Kulenović}, {\it G. Ladas} and {\it N. R. Prokup} [Comput. Math. Appl. 41, No. 5--6, 671--678 (2001; Zbl 0985.39017)]. A certain change of variable is given to simplify the equations. It is shown that zero is always an equilibrium point which satisfies a necessary and suffient condition for its local asymptotic stability. With a specific assumption on the parameters, there is a unique positive equilibrium point whose global stability is discussed. The authors examine the nature of semicycles of solutions and discuss invariant intervals.

37B40Topological entropy
37B20Notions of recurrence
37E99Low-dimensional dynamical systems
39A30Stability theory (difference equations)