Geodesic
A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
Annales Polonici Mathematici, Tome 62 (1995) no. 1, pp. 45-74

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The following problem of Markus and Yamabe is answered affirmatively: Let f be a local diffeomorphism of the euclidean plane whose jacobian matrix has negative trace everywhere. If f(0) = 0, is it true that 0 is a global attractor of the ODE dx/dt = f(x)? An old result of Olech states that this is equivalent to the question if such an f is injective. Here the problem is treated in the latter form by means of an investigation of the behaviour of f near infinity.
DOI : 10.4064/ap-62-1-45-74
Keywords: Markus-Yamabe conjecture, asymptotic behaviour of solutions of ODE's, immersions, embeddings, injectivity of mappings, curve lifting, foliations

Robert Feßler 1

1 
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Robert Feßler. A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization. Annales Polonici Mathematici, Tome 62 (1995) no. 1, pp. 45-74. doi: 10.4064/ap-62-1-45-74

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