A class of functions {g(x)} will be provided, such that the differential equation d^2x/dt^2+ g(x) = p(t) possesses an infinitely many number of invariant tori in the orbit space(t, x,dx/dt)∈S^1×R^2. Moreover, ea...A class of functions {g(x)} will be provided, such that the differential equation d^2x/dt^2+ g(x) = p(t) possesses an infinitely many number of invariant tori in the orbit space(t, x,dx/dt)∈S^1×R^2. Moreover, each solution of the equation is bounded. The proof is basedon the twist theorem.展开更多
A class of weaker nondegeneracy conditions is given and an existence theorem of invariant tori is prove n for small perturbations of degenerate integrable infinite dimensional Hamiltonian systems under the weaker nond...A class of weaker nondegeneracy conditions is given and an existence theorem of invariant tori is prove n for small perturbations of degenerate integrable infinite dimensional Hamiltonian systems under the weaker nondegeneracy conditions. The measure estimates of the parameter set are also given for which invariant tori exist. It is valuable to point out that by the motivation of finite dimensional situation the nondegeneracy conditions may be the weakest. Mainly KAM machine is used to prove the existence of invariant tori. The measure estimates for small divisor conditions, on which the measure estimates of the parameter set are based, will be given in the second paper.展开更多
We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional torus up to <k, ω> where ω is the frequency vector of the torus. That means the normal ...We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional torus up to <k, ω> where ω is the frequency vector of the torus. That means the normal frequencies with a difference <k,ω> may be regarded as the same. As an application, we derive a persistence is partially violated.展开更多
文摘A class of functions {g(x)} will be provided, such that the differential equation d^2x/dt^2+ g(x) = p(t) possesses an infinitely many number of invariant tori in the orbit space(t, x,dx/dt)∈S^1×R^2. Moreover, each solution of the equation is bounded. The proof is basedon the twist theorem.
基金the National Natural Science Foundation of China.
文摘A class of weaker nondegeneracy conditions is given and an existence theorem of invariant tori is prove n for small perturbations of degenerate integrable infinite dimensional Hamiltonian systems under the weaker nondegeneracy conditions. The measure estimates of the parameter set are also given for which invariant tori exist. It is valuable to point out that by the motivation of finite dimensional situation the nondegeneracy conditions may be the weakest. Mainly KAM machine is used to prove the existence of invariant tori. The measure estimates for small divisor conditions, on which the measure estimates of the parameter set are based, will be given in the second paper.
基金The work was supported by the National Natural Science Foundation of China (Grant Nos. 19925107 and 19701007 ) the Special Funds for Major State Basic Research Projects(973 Projects).
文摘We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional torus up to <k, ω> where ω is the frequency vector of the torus. That means the normal frequencies with a difference <k,ω> may be regarded as the same. As an application, we derive a persistence is partially violated.
