TY - JOUR
T1 - On the regularization of the collision solutions of the one-center problem with weak forces
AU - Castelli, Roberto
AU - Terracini, Susanna
PY - 2011/12
Y1 - 2011/12
N2 - We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. With this technique, we prove that the extended ow, where collision solutions are replaced with transmission trajectories, is continuous, though not differentiable, with respect to the initial data.
AB - We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. With this technique, we prove that the extended ow, where collision solutions are replaced with transmission trajectories, is continuous, though not differentiable, with respect to the initial data.
KW - Logarithmic potential
KW - Regularization technique
KW - Two-body problem
KW - Weak singular potential
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U2 - 10.3934/dcds.2011.31.1197
DO - 10.3934/dcds.2011.31.1197
M3 - Article
AN - SCOPUS:84859519813
VL - 31
SP - 1197
EP - 1218
JO - Discrete and Continuous Dynamical Systems. Series A
JF - Discrete and Continuous Dynamical Systems. Series A
SN - 1078-0947
IS - 4
ER -