A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
From MaRDI portal
Publication:2386872
DOI10.12775/TMNA.2005.004zbMath1101.58012arXivmath/0311147WikidataQ115239574 ScholiaQ115239574MaRDI QIDQ2386872
Alessandro Portaluri, Jacobo Pejsachowicz, Monica Musso
Publication date: 25 August 2005
Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0311147
(Semi-) Fredholm operators; index theories (47A53) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Spectral flows (58J30) Forms (bilinear, sesquilinear, multilinear) (47A07)
Related Items
Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations ⋮ The Maslov index and the spectral flow-revisited ⋮ A multiplicity result for a class of strongly indefinite asymptotically linear second order systems ⋮ Remarks on criticality and crisis in pure exchange economies ⋮ The Maslov index in weak symplectic functional analysis ⋮ Bifurcation of critical points for continuous families of \(C^2\) functionals of Fredholm type ⋮ Index theorems for graph-parametrized optimal control problems ⋮ An index theory for asymptotic motions under singular potentials ⋮ Index theory for heteroclinic orbits of Hamiltonian systems ⋮ Spectral flow, Brouwer degree and Hill's determinant formula ⋮ A generalized index theory for non-Hamiltonian system ⋮ A \(K\)-theoretical invariant and bifurcation for a parameterized family of functionals ⋮ Morse-Smale index theorems for elliptic boundary deformation problems ⋮ Linear instability of periodic orbits of free period Lagrangian systems ⋮ A 𝐾-theoretic proof of the Morse index theorem in semi-Riemannian geometry ⋮ Sturm theory with applications in geometry and classical mechanics ⋮ Linear instability for periodic orbits of non-autonomous Lagrangian systems ⋮ Yet another proof of the Morse index theorem ⋮ Jacobi fields in optimal control: Morse and Maslov indices ⋮ The Maslov Index in Symplectic Banach Spaces ⋮ A Morse-Smale index theorem for indefinite elliptic systems and bifurcation ⋮ Morse index and bifurcation ofp-geodesics on semi Riemannian manifolds ⋮ A family index theorem for periodic Hamiltonian systems and bifurcation ⋮ A bifurcation result for semi-Riemannian trajectories of the Lorentz force equation ⋮ Preservation of the Maslov index along bifurcating branches of solutions of first order systems in \(\mathbf {R}^{N}\) ⋮ Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory ⋮ Instability of semi-Riemannian closed geodesics