More Compactification for Differential Systems


This article is a review and promotion of the study of solutions of differential equations in the neighborhood of infinity via a non traditional compactification. We define and compute critical points at infinity of polynomial autonomuos differential systems and develop an explicit formula for the leading asymptotic term of diverging solutions to critical points at infinity. Applications to problems of completeness and incompleteness (the existence and nonexistence respectively of global solutions) of dynamical systems are provided. In particular a quadratic competing species model and the Lorentz equations are being used as arenas where our technique is applied. The study is also relevant to the Painlevé property and to questions of integrability of dynamical systems.

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H. Gingold and D. Solomon, "More Compactification for Differential Systems," Advances in Pure Mathematics, Vol. 3 No. 1A, 2013, pp. 190-203. doi: 10.4236/apm.2013.31A027.

Conflicts of Interest

The authors declare no conflicts of interest.


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