In all references on dynamical systems---encyclopedias, textbooks and articles---I have so far consulted, either

• there is from the beginning an emphasis on a certain class of dynamical system being studied (e.g. smooth dynamical systems or group actions), or
• the text is written very "high-level", without many concrete examples that illustrate the theory and without technically formulated theorems that carefully outline the various assumptions
• various viewpoints (dynamical vs. ergodic) and the definitions surrounding them aren't reconciled resp. contrasted (assuming they are introduced at all, such as a measure dynamical system)

Do you know of a text (ideally an advanced textbook) that does not suffer from these issues?

That would be a textbook that presents the theory as much as is possible in most general terms (meaning it develops the theory for dynamical systems $(G,X,\phi)$, where $G$ is a semigroup, $X$ a set and $\phi$ the evolution operator subject to the usual axioms) and then indicates exactly what further assumptions need to be made on $G$ and/or $X$ in order to obtain more specific theorems?

The first chapter of the first volume of Hasselblatt & Katok's "Handbook of Dynamical Systems" would come close, but unfortunately it is written (as is appropriate for an encyclopedic text) rather high-level with too few concrete examples to be helpful to me.
Something analogous to John Lee's trilogy of textbooks, "Introduction to Topological/Smooth/Riemannian Manifolds" would be what I'm looking for (ok, the last of the three book actually has a slightly different title, but let's not be pedantic :)), where one can first read up the theory for the general case (topological manifolds) and afterwards see in which direction the theory develops if one adds more structure (smoothnes, Riemannian metric).
Although the text I'm looking does not have to go that much into specialize topics, as Lee's books do, I would also be happy with a text (article, conference proceedings etc.) that stays with the foundational definitions and basic concepts and really clarifies the various relationships between them.