Dynamics of G-processes.

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 Equations9 (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 G. These processes are broad enough to include the G -actions (characterized as autonomous G -processes) and the two-parameter flows (where G = ℝ). We endow the space of G -processes with a natural group structure. We introduce the notions of orbit, pseudo-orbit and shadowing property for G -processes and analyze the relationship with the G -processes group structure. We study the equicontinuous G -processes and use it to construct nonautonomous G -processes with the shadowing property. We study the global solutions of the G -processes and the corresponding global shadowing property. We study the expansivity (global and pullback) of the G -processes. We prove that there are nonautonomous expansive G -processes and characterize the existence of expansive equicontinuous G -processes. We define the topological stability for G -processes and prove that every expansive G -process with the shadowing property is topologically stable. Examples of nonautonomous topologically stable G -processes are given. [ABSTRACT FROM AUTHOR]