Vassili Gelfreich, Warwick
<H3>High-precision computations of divergent asymptotic series and 
homoclinic phenomena</H3>

We study asymptotic expansions for
the exponentially small splitting of separatrices both from the analytical 
and numerical point of view.
Using analytic information, we can extract actual values of the 
coefficients of the series
numerically. The computations are performed with high-precision arithmetic, 
which involves up to several thousands digits. This approach
allows us to obtain information, which is usually considered to be out of 
reach of numerical methods. In particular, we use our results to test 
Borel-Laplace summability of the asymptotic series
and to study positions and types of singularities on the Borel plane.  In 
particular, we consider generalisations of the standard map, and 
Hamiltonian dynamical systems near a strong resonance.