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Asymptotics and expansions of solutions to an ordinary differential equation

A. D. Bruno


Abstract: We consider an ordinary differential equation of a very general form. We show how one can find the following objects by means of algorithms of Power Geometry: (i) all power asymptotics of solutions to the equation; (ii) all power logarithmic expansions of the solutions having the power asymptotics; (iii) all nonpower (exponential or logarithmic) asymptotics of solutions to the equation. We present the corresponding theory and algorithms and give examples of calculations of mentioned objects for an equation as well. The main attention is given to explanations of the computational algorithms.