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A dihedral Bott-type iteration formula and stability of symmetric periodic orbits
Motivated by the recent discoveries on the stability properties of symmetric periodic solutions of Hamiltonian systems, we establish a Bott-type iteration formula for dihedraly equivariant
Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit
In this paper, we prove Morse index theorem of Lagrangian systems with self-adjoint boundary conditions. Based on it, we give some nontrivial estimates on the difference of Morse indices. As an
Linear instability for periodic orbits of non-autonomous Lagrangian systems
Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the
Linear instability of periodic orbits of free period Lagrangian systems
In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general
Instability of semi-Riemannian closed geodesics
A celebrated result due to Poincare affirms that a closed non-degenerate minimizing geodesic $\gamma$ on an oriented Riemannian surface is hyperbolic. Starting from this classical theorem, our first