Periodic solutions and regularization of a Kepler problem with time-dependent perturbation
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- by Alberto Boscaggin, Rafael Ortega and Lei Zhao PDF
- Trans. Amer. Math. Soc. 372 (2019), 677-703 Request permission
Abstract:
We consider a Kepler problem in dimension two or three with a time-dependent $T$-periodic perturbation. We prove that for any prescribed positive integer $N$, there exist at least $N$ periodic solutions (with period $T$) as long as the perturbation is small enough. Here the solutions are understood in a general sense as they are allowed to have collisions. The concept of generalized solutions is defined intrinsically, and it coincides with the notion obtained in celestial mechanics via the theory of regularization of collisions.References
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Additional Information
- Alberto Boscaggin
- Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, I-10123 Torino, Italy
- MR Author ID: 896012
- Email: alberto.boscaggin@unito.it
- Rafael Ortega
- Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain
- Email: rortega@ugr.es
- Lei Zhao
- Affiliation: Institute of Mathematics, University of Augsburg, Universitätsstrasse 2, D-86159 Augsburg, Germany
- MR Author ID: 920078
- Email: lei.zhao@math.uni-augsburg.de
- Received by editor(s): December 13, 2017
- Received by editor(s) in revised form: April 8, 2018
- Published electronically: March 28, 2019
- Additional Notes: The first author acknowledges the support of the ERC Advanced Grant 2013 n. 339958, “Complex Patterns for Strongly Interacting Dynamical Systems - COMPAT”, and of the INDAM-GNAMPA Project “Dinamiche complesse per il problema degli $N$-centri”
The second author was partially supported by Spanish MINECO and ERDF project MTM2017-82348-C2-1-P
The third author was partially supported by NSFC No. 11601242, Fundamental Research Funds for the Central Universities of China, DFG FR 2637/2-1 and ZH 605/1-1 - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 677-703
- MSC (2010): Primary 37J45, 70F05, 70F16
- DOI: https://doi.org/10.1090/tran/7589
- MathSciNet review: 3968784