Titlebook: Elements of Topological Dynamics; J. Vries Book 1993 Springer Science+Business Media Dordrecht 1993 Compactification.differential equation

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ps with respect to problems that can be traced back to the qualitative theory of differential equa- is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ‘ rather than ‘Introduction . . . ‘) does not mean that this book should be compared, either in scope or i

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Various Aspects of the Theory of Dynamical Systems, attempt to explain the relationship of . with other parts of dynamical systems theory, notably . and . (also called the Theory of Smooth Dynamical Systems). Although in this chapter almost no ‘a(chǎn)bstract’ Topological Dynamics will be treated, we hope in this way to contribute to an understanding of i

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Continuous and Discrete Flows,y—but some recent material is added. A central role is played by ., in various forms. First, there is the theory of stability of invariant points and, more generally, invariant subsets (questions like: do they attract nearby orbits?). This topic will be almost neglected in this book. A second stabil

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Structure of Extensions, ‘lifted’ (by means of proximal extensions—even strongly proximal ones) to a RIM-extension of compact minimal flows. As proximal extensions are, from a dynamical point of view, close to isomorphisms (asymptotically, different points in any fiber cannot be distinguished), one expects that useful prop

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Various Aspects of the Theory of Dynamical Systems, attempt to explain the relationship of . with other parts of dynamical systems theory, notably . and . (also called the Theory of Smooth Dynamical Systems). Although in this chapter almost no ‘a(chǎn)bstract’ Topological Dynamics will be treated, we hope in this way to contribute to an understanding of its roots.

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