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)
The shadowing chain lemma for singular Hamiltonian systems involving strong forces. (English) Zbl 1269.37015
Summary: We consider a planar autonomous Hamiltonian system $\ddot q+\nabla V(q) = 0$, where the potential $V: \Bbb R^{2} \{\zeta \}\rightarrow \Bbb R$ has a single well of infinite depth at some point $\zeta $ and a strict global maximum 0 at two distinct points $a$ and $b$. Under a strong force condition around the singularity $\zeta $ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits -- the shadowing chain lemma -- via minimization of action integrals and using simple geometrical arguments.

37C29Homoclinic and heteroclinic orbits
37C50Approximate trajectories (pseudotrajectories, shadowing, etc.)
34C37Homoclinic and heteroclinic solutions of ODE
70H05Hamilton’s equations
Full Text: DOI