共查询到17条相似文献,搜索用时 125 毫秒
1.
p-Laplacian方程的Aubry-Mather集 总被引:1,自引:0,他引:1
本文通过引进合适的作用-角变量变换并结合新的估计方法,对p-Laplacian方程的Poincare映射应用推广的Aubry-Mather定理,证明了一类p-Laplacian方程的Aubry-Mather集的存在性. 相似文献
2.
本文通过引进适当的作用-角变量变换并结合新的估计方法,对超线性Duffing方程的Poincaré映射应用推广的Aubry-Mather定理,获得了一类超线性Duffing方程的Aubry-Mather集存在的充分性条件. 相似文献
3.
本文通过引进合适的作用— 角变量变换并结合新的估计方法, 对次线性不对称Duffing 方程的Poincaré 映射应用推广的Aubry-Mather 定理, 获得了一类次线性不对称Duffing 方程的Aubry-Mather 集存在的充分性条件. 相似文献
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通过引进合适的作用-角变量变换,并运用新的估计方法,对超线性不对称Duffing方程的Poincaré映射,应用推广的Aubry-Mather定理,证明了一类超线性不对称Duffing方程的Aubry-Mather集的存在性. 相似文献
5.
汪小明 《数学年刊A辑(中文版)》2015,36(4):355-366
通过引进合适的作用-角变量变换并结合新的估计方法,对次线性可逆系统的Poincare映射,应用推广的平面可逆系统的Aubry-Mather定理,在系统光滑性为C~1的情形下,获得了一类次线性可逆系统的Aubry-Mather集存在的充分条件. 相似文献
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推广了Mather关于正定Lagrange系统Aubry-Mather集在一维情形的存在性定理 ,同时给出了对平面Hamilton系统的一些应用. 相似文献
8.
In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbits connecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of the Lagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets and the global minimizer of the Lagrangian action. 相似文献
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Meiyue Jiang 《中国科学A辑(英文版)》1999,42(11):1121-1128
A result due to Mather on the existence of Aubry-Mather sets for superlinear positive definite Lagrangian systems is generalized
in one-dimensional case. Applications to existence of Aubry-Mather sets of planar Hamiltonian systems are given.
Project supported by the National Natural Science Foundation of China (Grant No. 19631020). 相似文献
12.
Hiroyoshi Mitake 《NoDEA : Nonlinear Differential Equations and Applications》2008,15(3):347-362
We investigate the large-time behavior of viscosity solutions of the Cauchy-Dirichlet problem (CD) for Hamilton-Jacobi equations
on bounded domains. We establish general convergence results for viscosity solutions of (CD) by using the Aubry-Mather theory.
相似文献
13.
MATHER SETS FOR SUBLINEAR DUFFING EQUATIONS 总被引:3,自引:0,他引:3
Qian Dingbian 《数学年刊B辑(英文版)》1994,15(4):421-434
MATHERSETSFORSUBLINEARDUFFINGEQUATIONS¥QIANDINGBIAN(DepartmentofMathematics,SuzhouUniversity,215006,China.)Abstract:Theexiste... 相似文献
14.
CHENG Wei & CHENGChongqing 《中国科学A辑(英文版)》2000,43(8):810-817
The exact monotone twist map of infinite cylinders in the Birkhoff region of instability is studied. A variational method
based on Aubry-Mather theory is used to discover infinitely many non-Birkhoff periodic orbits of fixed rotation number sufficiently
close to some irrational number for which the angular invariant circle does not exist. 相似文献
15.
Herman constructed an autonomous system of two degrees of freedom which says that in non-convex situations, oscillations do
happen and Aubry-Mather Theory cannot apply (see the results due to W. F. Chen in 1992). In this paper, it is shown that although
the orbits could visit a region far away from the initial point in phase space, they can only exist in some fixed regions
in I = (I
1, I
2) plane. Moreover, Aubry-Mather Theory can be applied outside the regions. 相似文献
16.
Diogo Aguiar Gomes 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(3-4):233-257
We extend the theory of Aubry-Mather measures to Hamiltonian systems that arise in vakonomic mechanics and sub-Riemannian
geometry. We use these measures to study the asymptotic behavior of (vakonomic) action-minimizing curves, and prove a bootstrapping
result to study the partial regularity of solutions of convex, but not strictly convex, Hamilton-Jacobi equations.
相似文献
17.
《应用数学年刊》2021,(3)
In this paper we apply KAM theory and the Aubry-Mather theory for twist maps to the study of bound geodesic dynamics of a perturbed blackhole background. The general theories apply mainly to two observable phenomena:the photon shell(unstable bound spherical orbits) and the quasi-periodic oscillations(QPO). We prove that there is a gap structure in the photon shell that can be used to reveal information of the perturbation. 相似文献