Arnold diffusion in Hamiltonian systems with small dissipation

CDSNS Colloquium
Monday, October 2, 2023 - 2:00pm for 1 hour (actually 50 minutes)
In-person in Skiles 005
Marian Gidea – Yeshiva University – Marian.Gidea@yu.edu
Alex Blumenthal

We consider a mechanical system consisting of a rotator and a pendulum, subject to a small, conformally symplectic perturbation. The resulting system has energy dissipation. We provide explicit conditions on the dissipation parameter, so that the resulting system exhibits Arnold diffusion. More precisely, we show that there are diffusing orbits along which the energy of the rotator grows by an amount independent of the smallness parameter. The fact that Arnold diffusion may play a role  in  systems with small dissipation was conjectured by Chirikov. Our system can be viewed as a simplified  model for an energy harvesting device, in which context the energy growth translates into generation of electricity.
Joint work with S.W. Akingbade and T-M. Seara.