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)
Extended Jury criterion. (English) Zbl 1189.37059
Summary: Algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli less than 1 directly from its coefficients. The form and the function of the criteria are similar to those of the Jury criterion which can be used to determine whether or not all the moduli of the roots of a real coefficient polynomial are less than 1.

37G15Bifurcations of limit cycles and periodic orbits
12Y05Computational aspects of field theory and polynomials
Full Text: DOI
[1] Jury I. Inners and Stability of Dynamic Systems. London: John Wiley, 1974 · Zbl 0307.93025
[2] Liang S, Zhang J. A complete discrimination system for polynomials with complex coefficients and its automatic generation. Sci China Ser E, 1999, 42: 113--128 · Zbl 0949.12002 · doi:10.1007/BF02917106
[3] Liao X. On asymptotic behavior of solutions to several classes of discrete dynamical systems. Sci China Ser A, 2002, 45: 432--442 · Zbl 1107.93029 · doi:10.1007/BF02872331
[4] Nian X. New criteria on the stability of interval discrete dynamic systems. Control Theory and Applications, 1999, 16: 558--561 · Zbl 1002.93045
[5] Wu Z, Liu W. Criterion of high-codimensional bifurcations with several pairs of purely imaginary eigenvalues. Linear Algebra Appl, 1997, 267: 53--63 · Zbl 0889.34035
[6] Zhang J, Yang L, Hou X. A criterion for dependency of algebraic equations with applications to automated theorem proving. Sci China Ser A, 1994, 37: 547--554 · Zbl 0820.68108