论文标题
接触谎言系统
Contact Lie systems
论文作者
论文摘要
我们定义和分析了触点谎言系统的属性，即一阶微分方程的系统，描述了$ t $依赖性的向量场的积分曲线，在汉密尔顿矢量场的有限维谎言代数中，相对于接触结构的有限维二元谎言代数。作为一个特别的例子，我们研究了保守的接触谎言系统的家庭。 liouville定理，接触降低和格罗莫夫非平方定理被开发并应用于接触式系统。我们的结果通过相关的物理和数学应用，例如Schwarz方程，Brockett Systems等。
We define and analyse the properties of contact Lie systems, namely systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of Hamiltonian vector fields relative to a contact structure. As a particular example, we study families of conservative contact Lie systems. Liouville theorems, contact reductions, and Gromov non-squeezing theorems are developed and applied to contact Lie systems. Our results are illustrated by examples with relevant physical and mathematical applications, e.g. Schwarz equations, Brockett systems, etcetera.
