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- W3208298350 abstract "We consider a perturbation of a central force problem of the form begin{equation*} ddot x = V'(|x|) frac{x}{|x|} + varepsilon ,nabla_x U(t,x), quad x in mathbb{R}^{2} setminus {0}, end{equation*} where $varepsilon in mathbb{R}$ is a small parameter, $Vcolon (0,+infty) to mathbb{R}$ and $Ucolon mathbb{R} times (mathbb{R}^{2} setminus {0}) to mathbb{R}$ are smooth functions, and $U$ is $tau$-periodic in the first variable. Based on the introduction of suitable time-maps (the radial period and the apsidal angle) for the unperturbed problem ($varepsilon=0$) and of an associated non-degeneracy condition, we apply an higher-dimensional version of the Poincar'{e}-Birkhoff fixed point theorem to prove the existence of non-circular $tau$-periodic solutions bifurcating from invariant tori at $varepsilon=0$. We then prove that this non-degeneracy condition is satisfied for some concrete examples of physical interest (including the homogeneous potential $V(r)=kappa/r^{alpha}$ for $alphain(-infty,2)setminus{-2,0,1}$). Finally, an application is given to a restricted $3$-body problem with a non-Newtonian interaction." @default.
- W3208298350 created "2021-11-08" @default.
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- W3208298350 date "2021-10-22" @default.
- W3208298350 modified "2023-09-27" @default.
- W3208298350 title "Periodic perturbations of central force problems and an application to a restricted $3$-body problem." @default.
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