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The homology of path spaces and Floer homology with conormal boundary conditions
Abstract.We define the Floer complex for Hamiltonian orbits on the cotangent bundle of a compact manifold which satisfy non-local conormal boundary conditions. We prove that the homology of this
Index theory for heteroclinic orbits of Hamiltonian systems
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic
A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi-Riemannian
Consider n = 2l ≥ 4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group Dl, where Dl is the group of
Morse Index and Linear Stability of the Lagrangian Circular Orbit in a Three-Body-Type Problem Via Index Theory
It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter β and on the eccentricity e of the orbit. We