A Lyapunov function for pullback attractors of nonautonomous differential equations.
A polynomial class of Markus-Yamabe counterexamples.
In the paper [CEGHM] a polynomial counterexample to the Markus-Yamabe Conjecture and to the discrete Markus-Yamabe Question in dimension n ≥ 3 are given. In the present paper we explain a way for obtaining a family of polynomial counterexamples containing the above ones. Finally we study the global dynamics of the examples given in [CEGHM].
A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
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.
Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system.
Asymptotic behaviour of positive solutions of the model which describes cell differentiation.
Asymptotic stability of switching systems.
Attractors for nonautonomous multivalued evolution systems generated by time-dependent subdifferentials.