共查询到20条相似文献,搜索用时 15 毫秒
1.
Peter Albers Urs Frauenfelder Felix Schlenk 《Journal of Differential Equations》2019,266(5):2466-2492
According to the Arnold conjectures and Floer's proofs, there are non-trivial lower bounds for the number of periodic solutions of Hamiltonian differential equations on a closed symplectic manifold whose symplectic form vanishes on spheres. We use an iterated graph construction and Lagrangian Floer homology to show that these lower bounds also hold for certain Hamiltonian delay equations. 相似文献
2.
Xiaoping Wang 《Journal of Mathematical Analysis and Applications》2003,286(2):664-674
In this paper, we obtain some new oscillation criteria for the difference equation with several delays
3.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(8):2660-2675
The numerical study of Dynamical Systems leads to obtain invariant objects of the systems such as periodic orbits, invariant tori, attractors and so on, that helps to the global understanding of the problem. In this paper we focus on the rigorous computation of periodic orbits and their distribution on the phase space, which configures the so called skeleton of the system. We use Computer Assisted Proof techniques to make a rigorous proof of the existence and the stability of families of periodic orbits in two-degrees of freedom Hamiltonian systems, which provide rigorous skeletons of periodic orbits. To that goal we show how to prove the existence and stability of a huge set of discrete initial conditions of periodic orbits, and later, how to prove the existence and stability of continuous families of periodic orbits. We illustrate the approach with two paradigmatic problems: the Hénon–Heiles Hamiltonian and the Diamagnetic Kepler problem. 相似文献
4.
We investigate multiple periodic solutions of convex asymptotically linear autonomous Hamiltonian systems. Our theorem generalizes a result by Mawhin and Willem. 相似文献
5.
运用集中紧性方法和Ekeland变分原理研究R^2中二阶渐近周期奇异Hamilton系统ue (1 g(t))V‘u(t,u)=0的极小问题,并证明该系统具有两条非平凡同宿轨道。 相似文献
6.
Meirong Xu 《Applied mathematics and computation》2010,217(1):441-449
In this paper, we study the difference equation:
7.
In this paper, we consider a class of impulsive Hamiltonian systems with a p‐Laplacian operator. Under certain conditions, we establish the existence of homoclinic orbits by means of the mountain pass theorem and an approximation technique. In some special cases, the homoclinic orbits are induced by the impulses in the sense that the associated non‐impulsive systems admit no non‐trivial homoclinic orbits. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
Guillaume James Pascal Noble Yannick Sire 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(4):1237-1264
We study relative periodic orbits (i.e. time-periodic orbits in a frame rotating at constant velocity) in a class of triatomic Euclidean-invariant (planar) Hamiltonian systems. The system consists of two identical heavy atoms and a light one, and the atomic mass ratio is treated as a continuation parameter. Under some nondegeneracy conditions, we show that a given family of relative periodic orbits existing at infinite mass ratio (and parametrized by phase, rotational degree of freedom and period) persists for sufficiently large mass ratio and for nearby angular velocities (this result is valid for small angular velocities). The proof is based on a method initially introduced by Sepulchre and MacKay [J.-A. Sepulchre, R.S. MacKay, Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators, Nonlinearity 10 (1997) 679–713] and further developed by Muñoz-Almaraz et al. [F.J. Muñoz-Almaraz, et al., Continuation of periodic orbits in conservative and Hamiltonian systems, Physica D 181 (2003) 1–38] for the continuation of normal periodic orbits in Hamiltonian systems. Our results provide several types of relative periodic orbits, which extend from small amplitude relative normal modes [J.-P. Ortega, Relative normal modes for nonlinear Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 665–704] up to large amplitude solutions which are not restrained to a small neighborhood of a stable relative equilibrium. In particular, we show the existence of large amplitude motions of inversion, where the light atom periodically crosses the segment between heavy atoms. This analysis is completed by numerical results on the stability and bifurcations of some inversion orbits as their angular velocity is varied. 相似文献
9.
Changfeng Gui 《Frontiers of Mathematics in China》2008,3(2):195-204
Using the Hamiltonian identities and the corresponding Hamiltonian constants for entire solutions of elliptic partial differential
equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties
of the solutions such as formulas for contact angles at infinity of concentration curves.
相似文献
10.
11.
We first establish Maslov index for non-canonical Hamiltonian system by using symplectic transformation for Hamiltonian system. Then the existence of multiple periodic solutions for the non-canonical Hamiltonian system is obtained by applying the Maslov index and Morse theory. As an application of the results, we study a class of non-autonomous differential delay equation which can be changed to non-canonical Hamiltonian system and obtain the existence of multiple periodic solutions for the equation by employing variational method. 相似文献
12.
13.
Let with h analytic of small norm. The problem of Arnold's diffusion consists in finding conditions on h which guarantee the existence of orbits Q of with connecting two arbitrary points of frequency space. Recently, J. N. Mather has found a sufficient condition for Arnold's
diffusion; this condition is not read on h itself, but on the set of all action-minimizing orbits of . In this paper we try to characterize those action-minimizing orbits whose mean frequency is close to periodic.
Received: November 26, 1996 相似文献
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15.
In this paper, we develop Kaplan-Yorke's method and consider the existence of periodic solutions for delay differential equations with two delays. Especially, we study Hopf and saddle-node bifurcations of periodic solutions for the equation with parameters, and give conditions under which the bifurcations occur. 相似文献
16.
Tianqing An 《Journal of Mathematical Analysis and Applications》2004,295(1):144-152
This paper discusses the existence and multiplicity of periodic orbits of Hamiltonian systems on symmetric positive-type hypersurfaces. We prove that each such energy hypersurface carries at least one symmetric periodic orbit. Under some suitable pinching conditions, we also get an existence result of multiple symmetric periodic orbits. 相似文献
17.
In this paper, the existence of homoclinic orbits for the second-order Hamiltonian systems without periodicity is studied and infinitely many homoclinic orbits for both superlinear and asymptotically linear cases are obtained. 相似文献
18.
A.M. Zhilyaev 《Applied Mathematics Letters》1996,9(6):7-11
This paper attempts to give a practical method to compute global periodic solutions of autonomous Hamiltonian systems of arbitrary finite order. The proposed numerical method is based on continuation of solutions branching from equlibrium points and requires no iterations. Moreover, during computation of one-parameter families of periodic orbits, their possible bifurcations are determined as well. 相似文献
19.
Yuan Shan 《数学学报(英文版)》2015,31(11):1725-1738
In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin. 相似文献
20.
Leonid Berezansky Elena Braverman 《Journal of Mathematical Analysis and Applications》2006,324(2):1336-1355
New explicit conditions of exponential stability are obtained for the nonautonomous linear equation