arXiv subjects
Publications and source records attributed to M. Sabatini.
We give an account of the results about limit cycle's uniqueness for Liénard equations, from Levinson-Smith's one to the most recent ones. We present a new uniqueness theorem in the line of Sansone-Massera's geometrical approach.
We prove the asymptotic stability of the equilibrium solution of a class of vector Liénard equations by means of LaSalle invariance principle. The key hypothesis consists in assuming that the intersections of the manifolds in $\{\dot V = 0\}$ be isolated. We deduce an existence theorem for periodic solutions of periodically perturbed vector Liénard equations.
We prove a uniqueness result for limit cycles of a class of second order ODE's. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETBA}.
We show that divergence-free jacobian maps, recently considered in \cite{N}, \cite{S}, are actually shear maps.