On the Stability and Instability of Elliptic Equilibria and Invariant Quasi-Periodic Tori of Real Analytic Hamiltonians

Explore the mathematical analysis of elliptic equilibria and invariant quasi-periodic tori in real analytic Hamiltonian systems through this 55-minute conference talk by Bassam Fayad from the University of Maryland. Delve into the fundamental concepts of stability and instability theory as applied to these critical structures in dynamical systems, examining how real analytic Hamiltonians behave around equilibrium points and quasi-periodic orbits. Gain insights into the sophisticated mathematical techniques used to determine when these systems maintain their structural integrity or undergo destabilization, with particular focus on the analytical properties that govern their long-term behavior.