Periodic solutions for a prescribed-energy problem of singular Hamiltonian systems

Mitsuru Shibayama
2017 Discrete and Continuous Dynamical Systems. Series A  
We study the existence of periodic solutions for a prescribedenergy problem of Hamiltonian systems whose potential function has a singularity at the origin like −1/|q| α (q ∈ R N ). It is known that there exist generalized periodic solutions which may have collisions, and the number of possible collisions has been estimated. In this paper we obtain a new estimation of the number of collisions. Especially we show that the obtained solutions have no collision if N ≥ 2 and α > 1. 2010 Mathematics
more » ... ubject Classification. Primary: 70H12, 70F05; Secondary: 34C25.
doi:10.3934/dcds.2017116 fatcat:ynquebuceranrbvlm72gyg3qsm