Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ ...Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.展开更多
In this paper, we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Riissmann＇s nondegeneracy condition by an impro...In this paper, we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Riissmann＇s nondegeneracy condition by an improved KAM iteration, and the persisting invariant tori are Gevrey smooth, with the same Gevrey index as the Hamiltonian.展开更多
For a family of smooth functions, the author shows that, under certain generic conditions, all extremal(minimal and maximal) points are non-degenerate.
In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently clos...In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently close to the integrable ones preserve a large set of n-dimensional invariant tori.展开更多
文摘Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.
文摘In this paper, we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Riissmann＇s nondegeneracy condition by an improved KAM iteration, and the persisting invariant tori are Gevrey smooth, with the same Gevrey index as the Hamiltonian.
基金supported by the National Natural Science Foundation of China(Nos.11201222,11171146)the Basic Research Program of Jiangsu Province(No.BK2008013)a program of the Priority Academic Program Development of Jiangsu Province
文摘For a family of smooth functions, the author shows that, under certain generic conditions, all extremal(minimal and maximal) points are non-degenerate.
文摘In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently close to the integrable ones preserve a large set of n-dimensional invariant tori.
