Symmetric periodic solutions of symmetric Hamiltonians in 1: 1 resonance

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(q1,q2,p1,p2) = 1/2(q(1)(2)+p(1)(2))+1/2(q(2)(2)+p(2)(2))+aq(1)(4)+bq(1)(2)q(2)(2)+cq(2)(4) with three real parameters a,b, and c. Moreover, we characterize the stability of these periodic solutions as a 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.

Automated summary

The aim of this study is to analytically prove the existence of symmetric periodic solutions of a specific family of Hamiltonian systems and characterize their stability. Additionally, a first-order analytical approach for these symmetric periodic solutions is obtained. These families of periodic solutions are different from the ones found in existing literature.