A Maslov-type index theory for symplectic paths
From MaRDI portal
Publication:1386865
DOI10.12775/TMNA.1997.021zbMath0977.53075OpenAlexW2589485954MaRDI QIDQ1386865
Publication date: 27 March 2001
Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.12775/tmna.1997.021
Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Lagrangian submanifolds; Maslov index (53D12) Index theory for dynamical systems, Morse-Conley indices (37B30)
Related Items
On the index theories for second order Hamiltonian systems ⋮ Lower bound on the number of periodic solutions for asymptotically linear planar Hamiltonian systems ⋮ Subharmonic solutions of Hamiltonian systems and the Maslov-type index theory ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ Multiple periodic solutions for asymptotically linear ordinary differential equations with double resonance ⋮ Morse index and multiple solutions for the asymptotically linear Schrödinger type equation ⋮ Homoclinic orbits for first order Hamiltonian systems with some twist conditions ⋮ Relative Morse index and multiple homoclinic orbits for a nonperiodic Hamiltonian system ⋮ Relative Morse index theory without compactness assumption ⋮ Index theory and multiple solutions for asymptotically linear second-order delay differential equations ⋮ A new index theory for linear self-adjoint operator equations and its applications ⋮ Relative Morse index and multiple solutions for a non-periodic Dirac equation with external fields ⋮ Index theory and multiple solutions for asymptotically linear wave equation ⋮ Some abstract critical point theorems for self-adjoint operator equations and applications ⋮ Multiple periodic solutions for asymptotically linear Duffing equations with resonance ⋮ Maslov \(P\)-index theory for a symplectic path with applications ⋮ Index iteration theories for periodic orbits: old and new ⋮ Closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\). ⋮ Hyperbolic characteristics on star-shaped hypersurfaces ⋮ Nonautonomous nonlinear ODEs: nonresonance conditions and rotation numbers ⋮ A new index theory for \(\mathrm{GL}^{+}(2)\)-paths with applications to asymptotically linear systems ⋮ Gutzwiller's semiclassical trace formula and Maslov-type index theory for symplectic paths ⋮ Multiple solutions for an asymptotically linear Duffing equation with Neumann boundary value conditions ⋮ A twist condition and multiple solutions of unbounded self-adjoint operator equation with symmetries ⋮ Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations ⋮ Multiple periodic solutions for asymptotically linear Duffing equations with resonance. II. ⋮ Multiple brake orbits in bounded convex symmetric domains ⋮ Index iteration theory for symplectic paths and multiple periodic solution orbits ⋮ Closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb R^{2n}\) ⋮ An optimal increasing estimate of the iterated Maslov-type indices ⋮ \( \omega^+\)-type index of \(\mathrm{GL}^+(2)\)-paths ⋮ The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems ⋮ INFINITELY MANY EVEN PERIODIC SOLUTIONS OF LAGRANGIAN SYSTEMS ON ANY RIEMANNIAN TORI WITH EVEN POTENTIAL IN TIME ⋮ Hyperbolic closed characteristics on compact convex smooth hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ On the equivalence of multiplicative structures in Floer homology and quantum homology ⋮ A review of the index method in closed geodesic problem ⋮ Topological structures of \(\omega\)-subsets in symplectic groups ⋮ Normal forms of symplectic matrices ⋮ Multiple periodic orbits of asymptotically linear autonomous convex Hamiltonian systems ⋮ An index theory with applications to homoclinic orbits of Hamiltonian systems and Dirac equations ⋮ Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics ⋮ Iteration inequalities of the Maslov-type index theory with applications ⋮ Birth-and-death \(Q\)-matrix problem with instantaneous states ⋮ The relation of the Morse index of closed geodesics with the Maslov-type index of symplectic paths ⋮ On the Morse index of Lagrangian systems. ⋮ Infinitely many periodic solution orbits of autonomous Lagrangian systems on tori
