Marian Gîdea
Yeshiva University, New York City. USA

We consider a Hamiltonian system subject to small, time dependent, conformally symplectic perturbation. One may expect such a system to manifest energy dissipation. Surprisingly, we show that the system exhibits orbits whose energy grows by a significant amount, provided that the perturbation satisfies some explicit conditions that hold generically. This result generalizes the Arnold diffusion problem in Hamiltonian systems to the case of systems with small dissipation. This is related to a conjecture by Chirkov asserting that Arnold diffusion may play a role in systems with small dissipation.