确定性混杂系统的极限和Morse集
Limit and Morse Sets for Deterministic Hybrid Systems
摘要：
术语“混合系统”是指在离散时间间隔经历马尔可夫扰动的连续时间动力系统。在本文中，我们发现在正确的表述下，一个混杂系统可以被看作是一个紧空间上的动力系统。这使得人们可以研究它的极限集。研究了混合系统的Morse分解，找到了非平凡Morse分解存在的一个充分条件，并研究了非平凡Morse分解的Morse集.最后，我们考虑的情况下，马尔可夫扰动是小的，表明在一个混合动力系统的轨迹与小扰动的行为类似的未扰动的动力系统。
英文摘要：
The term "hybrid system" refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical system on a compact space. This allows one to study its limit sets. We examine the Morse decompositions of hybrid systems, find a sufficient condition for the existence of a non-trivial Morse decomposition, and study the Morse sets of such a decomposition. Finally, we consider the case in which the Markovian perturbations are small, showing that trajectories in a hybrid system with small perturbations behave similarly to those of the unperturbed dynamical system.
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