Prescribed minimal period problems for convex Hamiltonian systems via Hofer-Zehnder symplectic capacity

2001 ◽  
Vol 236 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Evgeni Neduv
Keyword(s):  
Hamiltonian Systems ◽  
Minimal Period ◽  
Symplectic Capacity

Orbits with minimal period for a class of autonomous second order one-dimensional Hamiltonian systems

2018 ◽  
Vol 25 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Chouhaïd Souissi
Keyword(s):  
Periodic Solution ◽  
Hamiltonian System ◽  
Variational Method ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Minimal Period ◽  
One Dimensional ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractWe show, under an iterative condition which is similar to but stronger than that of Ambrosetti and Rabinowitz and by using a variational method, the existence of aT-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential\ddot{z}+V^{\prime}(z)=0,\quad z\in\mathbb{R},for any{T>0}. Moreover, such a solution has{T/k}as a minimal period for some integer{1\leq k\leq 3}.

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