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Morse Index, Stability and Spectral Bounds for Periodic Orbits in Reversible Lagrangian Systems
Alessandro Portaluri, Li Wu
We prove quantitative stability and instability estimates for reversible periodic solutions of strictly Legendre-convex Lagrangian systems. If the configuration dimension is , t…
Index theory for singular Lagrangian systems and Bessel-type differential operators
Xijun Hu, Alessandro Portaluri, Li Wu
The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Besse…
The fibered rotation number for ergodic symplectic cocycles and its applications: I. Gap Labelling Theorem
Xianzhe Li, Li Wu
Let be an ergodic topological dynamical system. The fibered rotation number for cocycles in , acting on $ Θ\times \mathbb{R}\mathbb…
Non-minimality and instability of brake orbits for natural Lagrangians on Riemannian manifolds
Luca Asselle, Xijun Hu, Alessandro Portaluri +1
We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit…