In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will sur...In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.展开更多
For a monotone twist map,under certain non-degenerate condition,we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation numb...For a monotone twist map,under certain non-degenerate condition,we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number,which indicates chaotic dynamics.Our results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus.展开更多
In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an esti...In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied by the invariant tori in the phase space. On an invariant torus,numerical solutions are quasi-periodic with a diophantine frequency vector of time step size dependence. These results generalize Shang's previous ones(1999, 2000), where the non-degeneracy condition is assumed in the sense of Kolmogorov.展开更多
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 t...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 = (I1 , I2 ) plane. Moreover, Aubry-Mather Theory can be applied outside the regions.展开更多
In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-peri...In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-periodic in t with Diophantine frequency.A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.展开更多
文摘In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.
基金Supported by National Key R&D Program of China(Grant No.2020YFA0713303)the Fundamental Research Funds for the Central Universities(Grant No.63213032)Nankai Zhide Foundation。
文摘For a monotone twist map,under certain non-degenerate condition,we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number,which indicates chaotic dynamics.Our results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus.
基金supported by National Natural Science Foundation of China(Grant No.11671392)
文摘In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied by the invariant tori in the phase space. On an invariant torus,numerical solutions are quasi-periodic with a diophantine frequency vector of time step size dependence. These results generalize Shang's previous ones(1999, 2000), where the non-degeneracy condition is assumed in the sense of Kolmogorov.
基金Project Supported by the Graduate Student Research Fellowship of Jiangsu Province of China (No.CX10B_002Z)
文摘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 = (I1 , I2 ) plane. Moreover, Aubry-Mather Theory can be applied outside the regions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11801295,11971059,12101623)China Postdoctoral Science Foundation(Grant No.2020M680132)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515110382)。
文摘In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-periodic in t with Diophantine frequency.A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.
