A G-process is briefly a process ([A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, Vol. 182 (Springer, 2013)], [C. M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971) 239–252], [P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Mathematical Surveys and Monographs, Vol. 176 (Amer. Math. Soc., 2011)]) for which the role of evolution parameter is played by a general topological group [Formula: see text]. These processes are broad enough to include the [Formula: see text]-actions (characterized as autonomous [Formula: see text]-processes) and the two-parameter flows (where [Formula: see text]). We endow the space of [Formula: see text]-processes with a natural group structure. We introduce the notions of orbit, pseudo-orbit and shadowing property for [Formula: see text]-processes and analyze the relationship with the [Formula: see text]-processes group structure. We study the equicontinuous [Formula: see text]-processes and use it to construct nonautonomous [Formula: see text]-processes with the shadowing property. We study the global solutions of the [Formula: see text]-processes and the corresponding global shadowing property. We study the expansivity (global and pullback) of the [Formula: see text]-processes. We prove that there are nonautonomous expansive [Formula: see text]-processes and characterize the existence of expansive equicontinuous [Formula: see text]-processes. We define the topological stability for [Formula: see text]-processes and prove that every expansive [Formula: see text]-process with the shadowing property is topologically stable. Examples of nonautonomous topologically stable [Formula: see text]-processes are given.

中文翻译：

---

G过程的动力学

G 过程简单地说是一个过程（[AN Carvalho, JA Langa 和 JC Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, Vol. 182 (Springer, 2013)], [CM Dafermos, An invariance紧致过程原理，J. 微分方程 9 (1971) 239–252]，[PE Kloeden 和 M. Rasmussen，非自治动力系统，数学调查和专着，第 176 卷（美国数学学会，2011 年）]）其中演化参数的作用是由一个一般拓扑群[公式：见正文]。这些过程足够广泛，可以包括 [公式：参见文本]-动作（表征为自主的 [公式：参见文本]-过程）和双参数流程（其中 [公式：参见文本]）。我们赋予[公式：见正文]-进程空间一个自然的组结构。我们介绍了[公式：见文本]-进程的轨道、伪轨道和阴影属性的概念，并分析了与[公式：见文本]-进程组结构的关系。我们研究了等连续的[公式：见文本]-过程，并用它来构造具有阴影属性的非自治[公式：见文本]-过程。我们研究了[公式：见正文]过程的全局解决方案和相应的全局阴影属性。我们研究[公式：见文本]过程的扩展性（全局和回调）。我们证明了存在非自治的扩展[公式：见文本]-过程，并表征了扩展等连续[公式：见文本]-过程的存在。我们定义了 [公式：见文本] 过程的拓扑稳定性，并证明了每个可扩展的 [公式：见正文]-具有阴影属性的过程是拓扑稳定的。给出了非自治拓扑稳定[公式：见正文]过程的例子。