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The dynamical systems approach to differential equations. (English) Zbl 0541.34026
This paper contains three chapters, as follows: Chapter I: Historical background; Chapter II: Convergence, chaos and stability; Chapter III: Convergence and stability in monotone flows. The author gives a remarkable survey of the basic themes in dynamical systems theory. Exemplifying theorems applied to the real world and some recent results are also presented.
Reviewer: N.H.Pavel

MSC:
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
37C10 Dynamics induced by flows and semiflows
00A30 Philosophy of mathematics
47H20 Semigroups of nonlinear operators
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
37N99 Applications of dynamical systems
37C75 Stability theory for smooth dynamical systems
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
01A45 History of mathematics in the 17th century
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