Heteroclinic orbits and heteroclinic chains for a discrete Hamiltonian system

2010 ◽  
Vol 53 (6) ◽  
pp. 1555-1564 ◽  
Author(s):  
Hao Zhang ◽  
ZhiXiang Li
Keyword(s):  
Hamiltonian System ◽  
Heteroclinic Orbits ◽  
Discrete Hamiltonian System

Study on the Periodic Solutions to a Superquadratic Discrete Hamiltonian System Based on Mechanics

2013 ◽  
Vol 394 ◽  
pp. 92-95
Author(s):  
Da Wei Sun ◽  
Jia Rui Liu
Keyword(s):  
Hamiltonian System ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Existence Of Solution ◽  
Discrete Hamiltonian System ◽  
New Type ◽  
Discrete Type

This paper studies the periodic solutions to a superquadratic second-oder discrete type Hamiltonian system in the n dimensional Euclide space. By the variational methods and some discrete computional techniques, this paper proves the existence of solution to a new type discrete Hamiltonian system.

scholarly journals Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Xiaoping Wang
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Satisfying Condition ◽  
Sufficient Conditions ◽  
Homoclinic Solutions ◽  
First Order ◽  
Discrete Hamiltonian System

We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian systemΔx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n)has no solution(x(n),y(n))satisfying condition0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, whereμ,ν>1and1/μ+1/ν=1andα(n),β(n),andγ(n)are real-valued functions defined onℤ.

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