Below is the ascii version of the abstract for 08-227. The html version should be ready soon.

madeu Delshams, Gemma Huguet
Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems
(1080K, PDF)

ABSTRACT.  In the present paper we consider the case of a general $\cont{r+2}$ 
perturbation, for $r$ large enough, of an a priori unstable 
Hamiltonian system of $2+1/2$ degrees of freedom, and we provide 
explicit conditions on it, which turn out to be $\cont{2}$ generic 
and are verifiable in concrete examples, which guarantee the 
existence of Arnold diffusion. 
This is a generalization of the result in Delshams et al., 
\emph{Mem. Amer. Math. Soc.}, 2006, where it was considered the case 
of a perturbation with a finite number of harmonics in the angular 
variables. 
The method of proof is based on a careful analysis of the geography 
of resonances created by a generic perturbation and it contains a 
deep quantitative description of the invariant objects generated by 
the resonances therein. The scattering map is used as an essential 
tool to construct transition chains of objects of different 
topology. The combination of quantitative expressions for both the 
geography of resonances and the scattering map provides, in a 
natural way, explicit computable conditions for instability.