Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I -- Method and Justification

Abstract

In this paper, we provide a systematic methodology for calculating multi-order asymptotic expansion of blow-up solutions near blow-up for autonomous ordinary differential equations (ODEs). Under the specific form of the principal term of blow-up solutions for a class of vector fields, we extract algebraic objects determining all possible orders in the asymptotic expansions. Examples for calculating concrete multi-order asymptotic expansions of blow-up solutions are finally collected.

78 pages. This is the first part in the present subject. Part II entitled "Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II - Dynamical Correspondence" is also uploaded (arXiv:2211.06868). In v2, unclear expressions are corrected