We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discre...We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.展开更多
In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z...In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z） is periodic in n and superlinear as {z} →4 ∞. We prove the existence and infinitely many （geometrically distinct） homoclonic orbits of the system by critical point theorems for strongly indefinite functionals.展开更多
The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the ba...The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.展开更多
基金supported by the Key Program of National Natural Science Foundation of China(Grant No.11232009)the National Natural Science Foundation ofChina(Grant Nos.11072218,11272287,and 11102060)+2 种基金the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)the Natural ScienceFoundation of Henan Province,China(Grant No.132300410051)the Educational Commission of Henan Province,China(Grant No.13A140224)
文摘We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.
基金CHEN WenXiong supported by Science Foundation of Huaqiao UniversityYANG Minbo was supported by Natural Science Foundation of Zhejiang Province (Grant No. Y7080008)+1 种基金YANG Minbo was supported by National Natural Science Foundation of China (Grant No. 11101374, 10971194)DING Yanheng was supported partially by National Natural Science Foundation of China (Grant No. 10831005)
文摘In this paper we consider the first order discrete Hamiltonian systems {x1（n＋1）-x1（n）=Hx2（n,x（n））,x2（n）-x2（n-1）=Hx1（n,x（n））,where x（n） = （x2（n）x1（n））∑ R^2N, H（n,z） = 1/2S（n）z. z ＋ R（n,z） is periodic in n and superlinear as {z} →4 ∞. We prove the existence and infinitely many （geometrically distinct） homoclonic orbits of the system by critical point theorems for strongly indefinite functionals.
基金Project supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209)the National Natural Science Foundation of China (Grant Nos. 90816001 and 11102060)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20093108110005)the Shanghai Subject Chief Scientist Project, China (Grant No. 09XD1401700)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)
文摘The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.
