0000000000754960

AUTHOR

Jaume Llibre

showing 2 related works from this author

Ejection and collision orbits of the spatial restricted three-body problem

1985

We begin by describing the global flow of the spatial two body rotating problem, μ=0. The remainder of the work is devoted to study the ejection and collision orbits when μ>-0. We make use of the ‘blow up’ techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S2×R. Also we find some particular collision-ejection orbits.

Applied MathematicsAstronomy and AstrophysicsTwo-body problemThree-body problemCollisionCelestial mechanicsComputational Mathematicssymbols.namesakeClassical mechanicsSpace and Planetary ScienceModeling and SimulationAutomotive EngineeringJacobian matrix and determinantsymbolsOrbit (dynamics)Astrophysics::Earth and Planetary AstrophysicsRemainderConstant (mathematics)Mathematical PhysicsMathematicsCelestial Mechanics
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An upper bound of the index of an equilibrium point in the plane

2012

Abstract We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index.

Equilibrium pointApplied MathematicsMathematical analysisGradient systemsUpper and lower boundsIndexsymbols.namesakesymbolsVector fieldLinear independenceHamiltonian systemsHamiltonian (quantum mechanics)AnalysisPlanar differential systemsMathematics
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