双向离散动力系统的局部稳定流形
Local Stable Manifold for the Bidirectional Discrete-Time Dynamics
摘要：
证明了双向离散非纯非线性Hamilton动力系统局部稳定流形的存在性。这是零是闭环特征值的情况，因此哈密顿矩阵是不可逆的。此外，我们给出了混合方向非线性哈密顿动力学的本征结构和辛性质。推广了具有双曲不动点的非线性离散Hamilton映射的局部稳定流形定理。作为结果，我们证明了局部解的存在性的动态规划方程，方程对应的离散时间最优控制问题。
英文摘要：
We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not invertible. In addition, we show the eigenstructure and the symplectic properties of the mixed direction nonlinear Hamiltonian dynamics. We extend the Local Stable Manifold Theorem for the nonlinear discrete-time Hamiltonian map with a hyperbolic fixed point. As a consequence, we show the existence of a local solution to the Dynamic Programming Equations, the equations corresponding to the discrete-time optimal control problem.
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