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Power geometry and four applications. (English) Zbl 0988.37020
The author proposes a calculus that can serve as an alternative to algebraic geometry, differential algebra, and group analysis. In particular, it includes four algorithms, their applications are shown in four problems. The author provides a detailed analysis of these problems. They are listed in the paper with numbers of their sections.

MSC:
37C10 Dynamics induced by flows and semiflows
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
37N05 Dynamical systems in classical and celestial mechanics
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37G05 Normal forms for dynamical systems
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