Minimal periodic solutions of first-order convex Hamiltonian systems with anisotropic growth

2018 ◽  
Vol 13 (5) ◽  
pp. 1063-1073 ◽  
Author(s):  
Chungen Liu ◽  
Li Zuo ◽  
Xiaofei Zhang
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Anisotropic Growth ◽  
First Order

scholarly journals Symmetric periodic solutions of symmetric Hamiltonians in 1:1 resonance

2020 ◽  
Author(s):  
Yocelyn Pérez ◽  
Claudio Vidal
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Analytical Approach ◽  
Hamiltonian Function ◽  
First Order ◽  
The Family ◽  
The Stability

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.

scholarly journals Periodic solutions of Hamiltonian systems with anisotropic growth

2010 ◽  
Vol 9 (4) ◽  
pp. 1069-1082 ◽  
Author(s):  
Tianqing An ◽  
◽  
Zhi-Qiang Wang ◽  
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Anisotropic Growth
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