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In this paper we prove the existence of global sections of disk-type in non-regular and strictly convex energy levels of integrable and near-integrable Hamiltonian systems with two degrees of freedom. This extends a result of (Hofer et al. in Ann. Math.(2) 148(1):197–289, 1998) where the same statement is true provided the energy level is regular. 相似文献
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Clodoaldo Grotta-Ragazzo 《Journal of Differential Equations》2006,220(1):259-278
We consider Hamiltonian systems with two degrees of freedom. We suppose the existence of a saddle-center equilibrium in a strictly convex component S of its energy level. Moser's normal form for such equilibriums and a theorem of Hofer, Wysocki and Zehnder are used to establish the existence of a periodic orbit in S with several topological properties. We also prove the explosion of the Conley-Zehnder index of any periodic orbit that passes close to the saddle-center equilibrium. 相似文献
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The authors study the bifurcation of homoclinic orbits from a degenerate homoclinic orbit in reversible system. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in two-dimensional manifolds. A perturbation technique for the detection of symmetric and nonsymmetric homoctinic orbits near the primary homoclinic orbits is developed. Some known results are extended. 相似文献
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The authors study the bifurcation of homoclinic orbits from a degenerate homoclinic
orbit in reversible system. The unperturbed system is assumed to have saddlecenter type equilibrium whose stable and unstable manifolds intersect in two-dimensional manifolds. A perturbation technique for the detection of symmetric and nonsymmetric homoclinic orbits near the primary homoclinic orbits is developed. Some known results are extended. 相似文献
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《Journal of Differential Equations》2004,203(2):185-215
We study homoclinic orbits to a saddle-center of a fourth-order ordinary differential equation, which is invariant under the transformation x→−x, involving an eigenvalue parameter q and an odd, piece-wise, cubic-type nonlinearity. It is found that for a sequence of eigenvalues which tends to infinity, homoclinic orbits exist whose complexity increases as the eigenvalue becomes larger. These orbits are found to be embedded in branches of homoclinic orbits to periodic orbits as x→±∞. 相似文献
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