Geodesic
Smoothness of unordered curves in two-dimensional strongly competitive systems
Applicationes Mathematicae, Tome 25 (1999) no. 4, pp. 449-455 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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It is known that in two-dimensional systems of ODEs of the form $\dotx^i=x^if^i(x)$ with ${\partial f^i}/{\partial x^j} 0$ (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We prove that such curves are in fact of class $C^1$.
DOI : 10.4064/am-25-4-449-455
Keywords: strongly competitive system of ordinary differential equations, invariant manifold, d-curve, Lotka-Volterra system

Janusz Mierczyński 1

1 
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Janusz Mierczyński. Smoothness of unordered curves in two-dimensional strongly competitive systems. Applicationes Mathematicae, Tome 25 (1999) no. 4, pp. 449-455. doi: 10.4064/am-25-4-449-455

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