A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
Volume 62 / 1995
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.
