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)
Averaging analysis of a perturbated quadratic center. (English) Zbl 0992.34024
The authors consider planar polynomial dynamical systems. Using the averaging theory for studying limit cycle bifurcations, they prove that if the quadratic system with a center at the origin dx/dt=-y(1+x), dy/dt=x(1+x) will be perturbed by polynomials of degree n to the polynomial systems dx/dt=-y(1+x)+εp(x,y), dy/dt=x(1+x)+εq(x,y), then for sufficiently small ε it is possible to obtain at most n hyperbolic limit cycles surrounding the origin.

34C07Theory of limit cycles of polynomial and analytic vector fields
34C29Averaging method
34C05Location of integral curves, singular points, limit cycles (ODE)
34C08Connections of ODE with real algebraic geometry
37G15Bifurcations of limit cycles and periodic orbits
34C23Bifurcation (ODE)