A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization

Volume 62 / 1995

Robert Feßler Annales Polonici Mathematici 62 (1995), 45-74 DOI: 10.4064/ap-62-1-45-74

Abstract

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.

Authors

  • Robert Feßler

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