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Growth and Decay Estimates near Non-Elementary Stationary Points

Published online by Cambridge University Press:  20 November 2018

Courtney Coleman
Courtney Coleman*
Affiliation:
Harvey Mudd College, Claremont, California
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 6 , 01 December 1970 , pp. 1156 - 1167
Copyright
Copyright © Canadian Mathematical Society 1970

References

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