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math.DS2026

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…

math.DS2025

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…

math.DS2025

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}\ma…