EVENT DETAILS AND ABSTRACT

Title: Lyapunov graph continuation
Speaker: Maria Bertolim
Speaker Info: Universidade de São Paulo
Brief Description:
Special Note:
Abstract:

In this work the Poincar\'{e}-Hopf inequalities are shown to be necessary and sufficient conditions for an abstract Lyapunov graph $L$ to be continued to an abstract Lyapunov graph of Morse type. The Lyapunov graphs considered may represent smooth flows on closed orientable $n$-manifolds, $n \geq 2$. The continuation which is presented by means of a constructive algorithm, is shown to be unique in dimensions two and three. In all other dimensions, the exact number of possible continuations of $L$ are presented.