论文标题
部分可观测时空混沌系统的无模型预测
Symmetries, conservation and dissipation in time-dependent contact systems
论文作者
论文摘要
在接触汉密尔顿系统中，所谓的消散数量类似于古典哈密顿系统中的保守量。在本文中，我们证明了非自动接触汉密尔顿系统的诺瑟定理，表征了一类与消散量的对称性的对称性。我们还研究了其他类别的对称性，这些对称性可以保留（最多达成共形因子）其他结构，例如接触形式或哈密顿函数。此外，利用扩展切线束的几何结构，我们引入了其他类别的对称性，以实现时间依赖时间的触点拉格朗日系统。我们的结果用几个例子说明了。特别是，我们提出了与时间有关的两体问题，这在天体力学中可能很有趣。
In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous contact Hamiltonian systems, characterizing a class of symmetries which are in bijection with dissipated quantities. We also study other classes of symmetries which preserve (up to a conformal factor) additional structures, such as the contact form or the Hamiltonian function. Furthermore, making use of the geometric structures of the extended tangent bundle, we introduce additional classes of symmetries for time-dependent contact Lagrangian systems. Our results are illustrated with several examples. In particular, we present the two-body problem with time-dependent friction, which could be interesting in celestial mechanics.
