Matches in SemOpenAlex for { <https://semopenalex.org/work/W2046684570> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W2046684570 endingPage "377" @default.
- W2046684570 startingPage "356" @default.
- W2046684570 abstract "Sitnikov proved the existence of oscillation and capture for a special motion of the restricted three-body problem, m, = 0 [ 141. Alekseev made a systematic study of this situation [ 11. He also proved the same result for all nonzero masses. (See Section 5 below for a discussion of this case.) A good exposition of this example following lectures of Conley is contained in [9] using the stable manifold result for a degenerately hyperbolic closed orbit of McGehee [ 81. Easton and McGehee proposed a planar three-body example with negative energy which could (possibly) exhibit similar oscillation and capture [3]. While Sitnikov’s example has two degrees of freedom, this planar example, after all the integrals and symmetries are removed, has three degrees of freedom. They studied a model example which completely decouples when the third body is near infinity and proved oscillation and capture exist for this model example. Their work left the following three steps undone: (1) show the parabolic orbits form a submanifold for the real equations, (2) show the a-parabolic orbits and w-parabolic orbits are transverse in a strong sense (see the definition of a hyperbolic homoclinic orbit defined below), and (3) show that symbolic dynamics can be used to show oscillation and capture exist using only the fact that the binary asymptotically decouples and not that it completely decouples when the third body is near infinity. For negative energy h, as the third particle goes to infinity parabolically, the asymptotic motion of q = r2 rl is that of a two-body problem with energy h. After regularization the set of all two-body motions with energy h < 0 is the Hopf flow on the three sphere, S3. Let IVs(S3) (resp. wU(S”)) be the set of w-parabolic orbits (resp. w-parabolic orbits). Easton has now shown that Ws(S3) and wl((S3) are Lipschitz manifolds [2]. This paper proves they are real analytic manifolds and “Cm at infinity” (at S”)" @default.
- W2046684570 created "2016-06-24" @default.
- W2046684570 creator A5055198027 @default.
- W2046684570 date "1984-05-01" @default.
- W2046684570 modified "2023-09-29" @default.
- W2046684570 title "Homoclinic orbits and oscillation for the planar three-body problem" @default.
- W2046684570 cites W1982380828 @default.
- W2046684570 cites W1988244564 @default.
- W2046684570 cites W1990626097 @default.
- W2046684570 cites W1992613502 @default.
- W2046684570 cites W2007695515 @default.
- W2046684570 cites W2034620513 @default.
- W2046684570 cites W2059625173 @default.
- W2046684570 cites W2070030217 @default.
- W2046684570 cites W2086983100 @default.
- W2046684570 cites W4212928962 @default.
- W2046684570 cites W4229596142 @default.
- W2046684570 cites W4239981491 @default.
- W2046684570 doi "https://doi.org/10.1016/0022-0396(84)90168-2" @default.
- W2046684570 hasPublicationYear "1984" @default.
- W2046684570 type Work @default.
- W2046684570 sameAs 2046684570 @default.
- W2046684570 citedByCount "32" @default.
- W2046684570 countsByYear W20466845702012 @default.
- W2046684570 countsByYear W20466845702014 @default.
- W2046684570 countsByYear W20466845702015 @default.
- W2046684570 countsByYear W20466845702016 @default.
- W2046684570 countsByYear W20466845702017 @default.
- W2046684570 countsByYear W20466845702019 @default.
- W2046684570 countsByYear W20466845702020 @default.
- W2046684570 crossrefType "journal-article" @default.
- W2046684570 hasAuthorship W2046684570A5055198027 @default.
- W2046684570 hasBestOaLocation W20466845701 @default.
- W2046684570 hasConcept C121332964 @default.
- W2046684570 hasConcept C121684516 @default.
- W2046684570 hasConcept C134306372 @default.
- W2046684570 hasConcept C134786449 @default.
- W2046684570 hasConcept C158622935 @default.
- W2046684570 hasConcept C200581526 @default.
- W2046684570 hasConcept C2778439541 @default.
- W2046684570 hasConcept C2781349735 @default.
- W2046684570 hasConcept C33923547 @default.
- W2046684570 hasConcept C41008148 @default.
- W2046684570 hasConcept C54355233 @default.
- W2046684570 hasConcept C62520636 @default.
- W2046684570 hasConcept C86803240 @default.
- W2046684570 hasConceptScore W2046684570C121332964 @default.
- W2046684570 hasConceptScore W2046684570C121684516 @default.
- W2046684570 hasConceptScore W2046684570C134306372 @default.
- W2046684570 hasConceptScore W2046684570C134786449 @default.
- W2046684570 hasConceptScore W2046684570C158622935 @default.
- W2046684570 hasConceptScore W2046684570C200581526 @default.
- W2046684570 hasConceptScore W2046684570C2778439541 @default.
- W2046684570 hasConceptScore W2046684570C2781349735 @default.
- W2046684570 hasConceptScore W2046684570C33923547 @default.
- W2046684570 hasConceptScore W2046684570C41008148 @default.
- W2046684570 hasConceptScore W2046684570C54355233 @default.
- W2046684570 hasConceptScore W2046684570C62520636 @default.
- W2046684570 hasConceptScore W2046684570C86803240 @default.
- W2046684570 hasIssue "3" @default.
- W2046684570 hasLocation W20466845701 @default.
- W2046684570 hasOpenAccess W2046684570 @default.
- W2046684570 hasPrimaryLocation W20466845701 @default.
- W2046684570 hasRelatedWork W1968181774 @default.
- W2046684570 hasRelatedWork W2046684570 @default.
- W2046684570 hasRelatedWork W2070055050 @default.
- W2046684570 hasRelatedWork W2157753588 @default.
- W2046684570 hasRelatedWork W2314121320 @default.
- W2046684570 hasRelatedWork W2321342552 @default.
- W2046684570 hasRelatedWork W2332879909 @default.
- W2046684570 hasRelatedWork W2358211602 @default.
- W2046684570 hasRelatedWork W2390134814 @default.
- W2046684570 hasRelatedWork W2913181415 @default.
- W2046684570 hasVolume "52" @default.
- W2046684570 isParatext "false" @default.
- W2046684570 isRetracted "false" @default.
- W2046684570 magId "2046684570" @default.
- W2046684570 workType "article" @default.