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math.DS2006
Stochastic inertial manifolds for damped wave equations
Zhenxin Liu
In this paper, stochastic inertial manifold for damped wave equations subjected to additive white noise is constructed by the Lyapunov-Perron method. It is proved that when the int…
math.DS2005
Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems
Zhenxin Liu
Chow, Li and Yi in [2] proved that the majority of the unperturbed tori {\it on sub-manifolds} will persist for standard Hamiltonian systems. Motivated by their work, in this paper…
math.DS2005★ 19 cited
The random case of Conley's theorem
Zhenxin Liu
The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow on the compact metric space , i.e. $X…