Preprint C59/2006
Robustly Transitive Sets in Nearly Integrable Hamiltonian Systems

DDIC

**Keywords: **
Robust transitivity | Symplectic diffeomorphism | Instability of Hamiltonian systems | Nearly integrable systems

We introduce $C^{r}$-open sets, $r=1, 2, \dots, \infty$, of symplectic diffeomorphisms and Hamiltonian systems
exhibiting \textit{large} robustly transitive sets.
As a consequence of the constructions we show that,
arbitrarily $C^{\infty}$-close to certain (nearly) integrable Hamiltonian systems with more than two degrees of freedom,
there exist systems with unbounded robustly transitive sets.