Geodesic
Growth and Decay Estimates near Non-Elementary Stationary Points
Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1156-1167

Voir la notice de l'article provenant de la source Cambridge University Press

Local growth and decay estimates near the stationary point at the origin are derived in § 3 for solutions of the vector system, (1) where A(x) and B(y) are homogeneous of degree m > 1 in the components of x and y, respectively, and f* and g* are of order greater than m in ‖(x, y)‖ near the origin. It is assumed that x = 0 is asymptotically stable and y = 0 is asymptotically unstable for the homogeneous systems of first approximation, (2) In order to derive the estimates in § 3, various results are needed concerning solutions of a homogeneous system such as (2) (a). These are derived in § 2 and are based on work of Hahn [4; 5], Lefschetz [8], and Zubov [12]. 
Coleman, Courtney. Growth and Decay Estimates near Non-Elementary Stationary Points. Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1156-1167. doi: 10.4153/CJM-1970-133-2
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