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 one-hour conference talk. Delve into the fundamental concepts of stability and instability theory as applied to these critical structures in dynamical systems. Examine the conditions under which elliptic equilibria maintain their stability properties and investigate scenarios where instability emerges. Learn about the behavior of invariant quasi-periodic tori and their role in the broader context of Hamiltonian dynamics. Gain insights into advanced mathematical techniques used to analyze these complex dynamical phenomena and understand their implications for the long-term evolution of Hamiltonian systems.