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

Corresponding Author:[email protected]

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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.
14 Dec 2020Submitted to Mathematical Methods in the Applied Sciences
15 Dec 2020Submission Checks Completed
15 Dec 2020Assigned to Editor
23 Dec 2020Reviewer(s) Assigned
06 Jun 2021Review(s) Completed, Editorial Evaluation Pending
07 Jun 2021Editorial Decision: Revise Minor
24 Jun 20211st Revision Received
24 Jun 2021Submission Checks Completed
24 Jun 2021Assigned to Editor
24 Jun 2021Reviewer(s) Assigned
08 Oct 2021Review(s) Completed, Editorial Evaluation Pending
18 Oct 2021Editorial Decision: Revise Minor
02 Nov 20212nd Revision Received
02 Nov 2021Submission Checks Completed
02 Nov 2021Assigned to Editor
03 Nov 2021Reviewer(s) Assigned
22 Apr 2022Review(s) Completed, Editorial Evaluation Pending
23 Apr 2022Editorial Decision: Revise Major
27 Apr 20223rd Revision Received
28 Apr 2022Submission Checks Completed
28 Apr 2022Assigned to Editor
29 Apr 2022Reviewer(s) Assigned
16 Jul 2022Review(s) Completed, Editorial Evaluation Pending
18 Jul 2022Editorial Decision: Accept