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)
Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria. (English) Zbl 0908.34034
Summary: For a class of Hamiltonian systems in $\bbfR^4$ the set of homoclinic and heteroclinic orbits which connect saddle-focus equilibria is studied using a variational approach. The oscillatory properties of a saddle-focus equilibrium and the variational nature of the problem give rise to connections in many homotopy classes of the configuration plane punctured at the saddle-foci. This variational approach does not require any assumptions on the intersections of stable and unstable manifolds, such as transversality. Moreover, these connections are shown to be local minimizers of an associated action functional. This result has applications to spatial pattern formation in a class of fourth-order bistable evolution equations.

34C37Homoclinic and heteroclinic solutions of ODE
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Full Text: DOI