TITLE:
On the use of Lyapunov exponents to detect global properties of the dynamics

AUTHOR:
Carles Sim\'o

Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona,
Gran Via, 585, 08071 Barcelona (Spain)

ABSTRACT:
Different methods have been proposed for the numerical computation of Lyapunov
exponents. After a quick review we shall describe a new powerful method which
is specially suitable to detect domains of ordered motions. Then several
examples will be presented, applied to conservative and non-conservative
systems, discrete and continuous. They show how one can obtain relevant
information on the global dynamics in a fast way. Finally, an application to
compute the metric entropy of a family of diffeomorphisms will be done. In
that case to have an accurate value of the entropy is important to support
different conjectures.