辛SubVolumes的动力学
Dynamics of Symplectic SubVolumes
摘要：
在本文中，我们将探讨的基本约束的演化所拥有的任何哈密顿相空间的某些辛子体积。本研究对最优控制和保守机械系统的控制有直接的应用。我们与辛拓扑的几何不变量的计算，可以很容易地进行与流图的状态转移阵。我们将展示如何某些辛子体积有一个最小的可获得的体积，进一步如果子体积的尺寸等于相空间尺寸，这个约束减少到刘维尔定理。最后，我们提出了一个首选的基础，对于一个给定的正则变换，具有一定的极小性质方面的局部体积膨胀的相空间。
英文摘要：
In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical systems. We relate geometric invariants of symplectic topology to computations that can easily be carried out with the state transition matrix of the flow map. We will show how certain symplectic subvolumes have a minimal obtainable volume; further if the subvolume dimension equals the phase space dimension, this constraint reduces to Liouville's Theorem. Finally we present a preferred basis that, for a given canonical transformation, has certain minimality properties with regards to the local volume expansion of phase space.
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