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Symmetric periodic solutions of symmetric Hamiltonians in 1:1 resonance
  • Yocelyn Pérez,
  • Claudio Vidal
Yocelyn Pérez
Universidad del Bio Bio
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Claudio Vidal
Universidad del Bio Bio
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Abstract

The aim of this work is to prove analytically the existence of symmetric periodic solutions of the family of Hamiltonian systems with Hamiltonian function H(q_1,q_2,p_1,p_2)= 1/2(q_1^2+p_1^2)+1/2(q_2^2+p_2^2)+ a q_1^4+b q_1^2q_2^2+c \q_2^4 with three real parameters a, b and c. Moreover, we characterize the stability of these periodic solutions as function of the parameters. Also, we find a first-order analytical approach of these symmetric periodic solutions. We emphasize that these families of periodic solutions are different from those that exist in the literature.

Peer review status:IN REVISION

14 Dec 2020Submitted to Mathematical Methods in the Applied Sciences
15 Dec 2020Assigned to Editor
15 Dec 2020Submission Checks Completed
23 Dec 2020Reviewer(s) Assigned
06 Jun 2021Review(s) Completed, Editorial Evaluation Pending
07 Jun 2021Editorial Decision: Revise Minor