22 papers
This paper introduces 0-shifted cosymplectic structures on differentiable stacks to develop a Hamiltonian action theory that includes a reduction procedure, a Kirwan convexity theorem, and examples of Morse-Bott Lie groupoid morphisms.
This paper establishes that non-constant periodic brake orbits in natural Lagrangian systems on Riemannian manifolds are never action minimizers and are generally linearly or spectrally unstable under specific dimensional and non-degeneracy conditions, a result derived by analyzing local index contributions via Seifert collar coordinates and illustrated through explicit computations for classical mechanical systems.