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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, UAMAzc., Av. San Pablo 180, Col. Reynosa, México D. F. 02200, Mexico 
2.  San Antonio 64, Col. Las Fuentes, Zapopan, Jalisco, 45070, Mexico 
$V$ 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 ${Cr}=\{\omega\in S^{n1}:\nabla V(\omega)=0\}$, $n\geq 3$, 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 zeroenergy 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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