Bifurcation and Forced Symmetry Breaking In Hamiltonian Systems (original) (raw)

This paper explores the persistence of relative equilibria in Hamiltonian systems under perturbations, focusing on the conditions required for these equilibria to remain stable when considering symmetries and their breaking. It establishes a series of theorems demonstrating the bijective correspondence between relative equilibria and critical points of certain smooth functions that characterize their behavior under perturbations. The findings entail significant implications for understanding how Hamiltonian systems behave in the presence of broken symmetries and provide groundwork for future explorations in symplectic geometry and dynamical systems.