Figure 1.
The restriction of a possible (according to Proposition 2) set $D$ to the strip $0\le t_0\le 2\pi$
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August
2018, 38(8): 3955-3975.
doi: 10.3934/dcds.2018172
Periodic linear motions with multiple collisions in a forced Kepler type problem
| 1. | Fac. Ciências da Univ. Lisboa e Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Campo Grande, Edifício C6, piso 2, P-1749-016 Lisboa, Portugal |
| 2. | Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Campo Grande, Edifício C6, piso 2, P-1749-016 Lisboa, Portugal |
In [
Mathematics Subject Classification:
Primary: 34C25; Secondary: 37E40, 70K40.
Citation:
Carlota Rebelo, Alexandre Simões. Periodic linear motions with multiple collisions in a forced Kepler type problem. Discrete and Continuous Dynamical Systems,
2018, 38
(8)
: 3955-3975.
doi: 10.3934/dcds.2018172
![]()
References:
| [1] |
P. Amster, J. Haddad, R. Ortega and A. J. Ureña,
Periodic motions in forced problems of Kepler type, NODEA, 18 (2011), 649-657.
doi: 10.1007/s00030-011-0111-8. |
| [2] |
F. Dalbono and C. Rebelo,
Poincaré-Birkhoff fixed point theorem and periodic solutions of asymptotically linear planar Hamiltonian systems, Turin Fortnight Lectures on Nonlinear Analysis, Rend. Sem. Mat. Univ. Politec. Torino, 60 (2002), 233-263.
|
| [3] |
J. Franks,
Generalizations of the Poincaré-Birkhoff theorem, Ann. of Math., 128 (1988), 139-151.
doi: 10.2307/1971464. |
| [4] |
M. W. Hirsch,
Differential Topology, Springer-Verlag, 1976. |
| [5] |
P. Le Calvez and J. Wang,
Some remarks on the Poincaré-Birkhoff theorem, Proc. of the AMS, 138 (2010), 703-715.
doi: 10.1090/S0002-9939-09-10105-3. |
| [6] |
S. Marò,
Periodic solution of a forced relativistic pendulum via twist dynamics, Topological Methods in Nonlinear Analysis, 42 (2013), 51-75.
|
| [7] |
R. Ortega,
Linear motions in a periodically forced Kepler problem, Portugaliae Mathematica, 68 (2011), 149-176.
doi: 10.4171/PM/1885. |
| [8] |
A. Simões, Bouncing solutions in a generalized Kepler problem, Master Thesis, University of Lisbon, 2016. |
| [9] |
H. L. Smith and P. Waltman,
The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511530043. |
| [10] |
H. J. Sperling,
The collision singularity in a perturbed two-body problem, Celestial Mechanics, 1 (1969/1970), 213-221.
doi: 10.1007/BF01228841. |
| [11] |
L. Zhao,
Some collision solutions of the rectilinear periodically forced Kepler problem, Adv. Nonlinear Stud., 16 (2016), 45-49.
doi: 10.1515/ans-2015-5021. |
show all references
References:
| [1] |
P. Amster, J. Haddad, R. Ortega and A. J. Ureña,
Periodic motions in forced problems of Kepler type, NODEA, 18 (2011), 649-657.
doi: 10.1007/s00030-011-0111-8. |
| [2] |
F. Dalbono and C. Rebelo,
Poincaré-Birkhoff fixed point theorem and periodic solutions of asymptotically linear planar Hamiltonian systems, Turin Fortnight Lectures on Nonlinear Analysis, Rend. Sem. Mat. Univ. Politec. Torino, 60 (2002), 233-263.
|
| [3] |
J. Franks,
Generalizations of the Poincaré-Birkhoff theorem, Ann. of Math., 128 (1988), 139-151.
doi: 10.2307/1971464. |
| [4] |
M. W. Hirsch,
Differential Topology, Springer-Verlag, 1976. |
| [5] |
P. Le Calvez and J. Wang,
Some remarks on the Poincaré-Birkhoff theorem, Proc. of the AMS, 138 (2010), 703-715.
doi: 10.1090/S0002-9939-09-10105-3. |
| [6] |
S. Marò,
Periodic solution of a forced relativistic pendulum via twist dynamics, Topological Methods in Nonlinear Analysis, 42 (2013), 51-75.
|
| [7] |
R. Ortega,
Linear motions in a periodically forced Kepler problem, Portugaliae Mathematica, 68 (2011), 149-176.
doi: 10.4171/PM/1885. |
| [8] |
A. Simões, Bouncing solutions in a generalized Kepler problem, Master Thesis, University of Lisbon, 2016. |
| [9] |
H. L. Smith and P. Waltman,
The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511530043. |
| [10] |
H. J. Sperling,
The collision singularity in a perturbed two-body problem, Celestial Mechanics, 1 (1969/1970), 213-221.
doi: 10.1007/BF01228841. |
| [11] |
L. Zhao,
Some collision solutions of the rectilinear periodically forced Kepler problem, Adv. Nonlinear Stud., 16 (2016), 45-49.
doi: 10.1515/ans-2015-5021. |
Figure 2.
Cylinder $B$
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