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The 3-dimensional cored and logarithm potencials: Periodic orits
Kulesza, Maite (Universidade Federal Rural de Pernambuco(Brasil). Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data: 2014
Resum: We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ε, we show that both systems give essentially the same set of equations of motion up to first order in ε. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ε, apply equally to both systems in every energy level H = h > 0. The averaging method used proves the existence of at most three periodic orbits, for ε small enough, and gives an analytic approximation for the initial conditions of these periodic orbits.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: periodic orbits ; galactic potential ; cored potential ; logarithm potential ; averaging theory
Publicat a: Journal of Mathematical Physics, Vol. 55 (2014) , p. 112702, ISSN 0022-2488

DOI: 10.1063/1.4901126

19 p, 727.0 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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