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)
Monodromy and stability for nilpotent critical points. (English) Zbl 1088.34021
The authors study the behavior near an isolated singularity at the origin of an analytic vector field $X$ on the plane for which the linear part $DX(0)$ has both eigenvalues zero, but is not itself zero (a “nilpotent singularity”). They give a new proof of a theorem of Andreev that characterizes which of such critical points are monodromic, meaning that there is a first return map defined on a section of the flow of the vector field with one endpoint at the origin. After introducing a special form for vector fields having a monodromic nilpotent singularity at the origin, they characterize, for several specialized cases, those singularities of this type that are in fact centers. Techniques used include index theory and the generalized trigonometric functions of Lyapunov.

34C05Location of integral curves, singular points, limit cycles (ODE)
34C23Bifurcation (ODE)
37C10Vector fields, flows, ordinary differential equations
Full Text: DOI