论文标题
一个离散的汉密尔顿 - 雅各比理论，联系汉密尔顿动态
A Discrete Hamilton--Jacobi Theory for Contact Hamiltonian Dynamics
论文作者
论文摘要
在本文中，我们提出了一个离散的汉密尔顿 - （离散的）汉密尔顿动力学的雅各比理论，该动态定义在（离散）接触歧管上。为此，我们首先提供了一种新颖的几何汉密尔顿 - 雅各比理论，用于连续接触汉密尔顿动力学。然后，扎根于离散的触点拉格朗日公式，我们通过离散的legendre变换获得了哈密顿动力学的离散方程。基于离散的触点汉密尔顿方程，我们构建了一个离散的汉密尔顿 - 雅各比方程，用于接触汉密尔顿动力学。我们展示了离散的汉密尔顿 - 雅各比方程与这项工作中介绍的雅各比理论如何相关。然后，我们提出了离散接触流的触点歧管上的离散汉密尔顿方程的几何基础。在本文的最后，我们提供了一个数值示例来测试理论。
In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton--Jacobi theory for continuous contact Hamiltonian dynamics. Then, rooting on the discrete contact Lagrangian formulation, we obtain the discrete equations for Hamiltonian dynamics by the discrete Legendre transformation. Based on the discrete contact Hamilton equation, we construct a discrete Hamilton--Jacobi equation for contact Hamiltonian dynamics. We show how the discrete Hamilton--Jacobi equation is related to the continuous Hamilton--Jacobi theory presented in this work. Then, we propose geometric foundations of the discrete Hamilton--Jacobi equations on contact manifolds in terms of discrete contact flows. At the end of the paper we provide a numerical example to test the theory.
