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Comparison among different notions of solution for the $p$-system at a junction
Spiral motion in classical mechanics
| 1. | Departamento de Ciencias Básicas, UAM-Azc., Av. San Pablo 180, Col. Reynosa, México D. F. 02200, Mexico |
| 2. | San Antonio 64, Col. Las Fuentes, Zapopan, Jalisco, 45070, Mexico |
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$V$ in dimension three, which exhibits an orbit that spirals as time goes to infinity. This kind of orbits cannot occur for this class of potentials in dimension two [4] or, see below, if ${Cr}=\{\omega\in S^{n-1}:\nabla V(\omega)=0\}$, $n\geq 3$, is totally disconnected. In addition, for each $\mu>2$ we give an example of a potential of the form $V(r,\theta)=O(r^{-\mu})$, in two dimensions, which is not radially symmetric and has a zero-energy orbit that escapes towards infinity in spirals. Zero energy orbits escaping towards infinity in spirals cannot occur for radial potentials with the same rate of decay.
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