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Some Collision Solutions of the Rectilinear Periodically Forced Kepler Problem
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zhao, Lei |
| Copyright Year | 2016 |
| Abstract | Abstract In [5], Ortega has analyzed “generalized” collision solutions of the periodically forced rectilinear Kepler problem. In this note, we explain a different approach to study these solutions by embedding the non-autonomous Hamiltonian system into the zero-energy level of an autonomous Hamiltonian system and by employing the Levi-Civita regularization to regularize the double collisions. In addition to this, under a certain smoothness hypothesis of the periodic force term, we show that there exists a set of positive measure of generalized quasi-periodic solutions in the extended phase space, each of them accumulated by generalized periodic solutions of the system. The energy of these quasi-periodic solutions can have an arbitrary large absolute value. |
| Starting Page | 45 |
| Ending Page | 49 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| DOI | 10.1515/ans-2015-5021 |
| Volume Number | 16 |
| Alternate Webpage(s) | http://www.cim.nankai.edu.cn/about_us/member/zhaol/pdf/1dperturbedkepler(ans).pdf |
| Alternate Webpage(s) | https://doi.org/10.1515/ans-2015-5021 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
