Generic bifurcations of second order ordinary differential equations on differentiable manifolds
Generic one-parameter families of vector fields on two-dimensional manifolds
Generic properties of the rotation number of one-parameter diffeomorphisms of the circle
Global attractor of a differentiable autonomous system on the plane
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.