In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the...In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field.展开更多
In this paper we reformulate a Lyapunov center theorem of infinite dimensional Hamiltonian systems arising from PDEs.The proof is based on a modified KAM iteration for periodic case.
In this paper,we consider the existence of analytic invariant curves of an iterative equation f(f(x))=xea-x-f(x)which arises from Ricker-type second-order equation.By reducing the equation with the Schr?der transforma...In this paper,we consider the existence of analytic invariant curves of an iterative equation f(f(x))=xea-x-f(x)which arises from Ricker-type second-order equation.By reducing the equation with the Schr?der transformation to an auxiliary equation,the author discusses not only that the parameter at resonance,i.e.,at a root of the unity,but also the parameter near resonance under the Brjuno condition.展开更多
In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive （n ＋ 2）-dimensional Lebesgue measure in the neighborhood of an elliptic ...In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive （n ＋ 2）-dimensional Lebesgue measure in the neighborhood of an elliptic equilibrium provided that its lineaxized system at the equilibrium satisfies some small divisor conditions. Both of the invariant sets are foliated by two-dimensional invaxiant tori carrying quasi-oeriodic solutions.展开更多
In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+...In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.展开更多
基金supported by PRIN 2015 Variational methods with applications to problems in mathematical physics and geometry
文摘In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field.
基金This study was funded by the National Natural Science Foundation of China(Nos.11871146 and 11671077).
文摘In this paper we reformulate a Lyapunov center theorem of infinite dimensional Hamiltonian systems arising from PDEs.The proof is based on a modified KAM iteration for periodic case.
基金the National Natural Science Foundation of China(Grant Nos.11671061,11971081)the Natural Science Foundation of Chongqing(Grant No.cstc2020jcyj-msxm X0857)+2 种基金Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN201800502,KJQN201900525)Foundation of youth talent of Chongqing Normal University(02030307-00039),the(Grant Nos.VEGA-MS 1/0358/20,VEGA-SAV 2/0127/20)the Slovak Research and Development Agency under the contract(Grant No.APVV-18-0308)。
文摘In this paper,we consider the existence of analytic invariant curves of an iterative equation f(f(x))=xea-x-f(x)which arises from Ricker-type second-order equation.By reducing the equation with the Schr?der transformation to an auxiliary equation,the author discusses not only that the parameter at resonance,i.e.,at a root of the unity,but also the parameter near resonance under the Brjuno condition.
基金Supported by NNSF of China (Grant 10531050)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070284004)
文摘In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive （n ＋ 2）-dimensional Lebesgue measure in the neighborhood of an elliptic equilibrium provided that its lineaxized system at the equilibrium satisfies some small divisor conditions. Both of the invariant sets are foliated by two-dimensional invaxiant tori carrying quasi-oeriodic solutions.
文摘In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.
