Determinacy of degenerate equilibria with linear part x'=y, y'= 0 using MACSYMA
Applied Mathematics and ComputationPublished 1 January 1987
Richard H. Rand, William L. Keith
Citations6
SJR quartileQ1
SJR score0.89
SNIP1.40
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Abstract
A MACSYMA program is presented which implements Takens's method for proving determinacy of a flow in the neighborhood of an equilibrium point by successive blowup transformations. The program is applied to nonlinear systems with linear part x'= y, y'= 0, and an examination of the pattern of the results reveals an infinite sequence of determinacy theorems. The results are applied to the behavior of van der Pol's equation at infinity.
Keywords
MathematicsPhysics and Astronomy
Applied mathematical sciencesNonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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