Given an integrable Hamiltonian ho with n-degrees of freedom and a Diophantme trequency ω, then, arbitrarily close to h0 in the C^r topology with r 〈 2n, there exists an analytical Hamiltonian he with no KAM torus o...Given an integrable Hamiltonian ho with n-degrees of freedom and a Diophantme trequency ω, then, arbitrarily close to h0 in the C^r topology with r 〈 2n, there exists an analytical Hamiltonian he with no KAM torus of rotation vector w. In contrast with it, KAM tori exist if perturbations are small in C^T topology with r 〉 2n.展开更多
文摘Given an integrable Hamiltonian ho with n-degrees of freedom and a Diophantme trequency ω, then, arbitrarily close to h0 in the C^r topology with r 〈 2n, there exists an analytical Hamiltonian he with no KAM torus of rotation vector w. In contrast with it, KAM tori exist if perturbations are small in C^T topology with r 〉 2n.
