The behavior of the index of a periodic linear Hamiltonian system under iteration

DOI10.1016/0001-8708(77)90107-4zbMath0362.58005OpenAlexW2094572099MaRDI QIDQ1239948

J. J. Duistermaat, Richard H. Cushman

Publication date: 1977

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(77)90107-4

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (17)

Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators ⋮ Symplectic classification of quadratic forms, and general Mehler formulas ⋮ Convex Hamiltonian energy surfaces and their periodic trajectories ⋮ The Morse and Maslov indices for Schrödinger operators ⋮ Index theorems for graph-parametrized optimal control problems ⋮ Path integration over closed loops and Gutzwiller's trace formula ⋮ Decomposition of spectral flow and Bott-type iteration formula ⋮ The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems ⋮ On a product formula for the Conley-Zehnder index of symplectic paths and its applications ⋮ The Maslov index and the spectra of second order elliptic operators ⋮ Algebraic Riccati equation and symplectic algebra ⋮ Closed geodesics and homogeneous spaces ⋮ Hyperbolic closed characteristics on compact convex smooth hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Spectral flow and bifurcation of critical points of strongly indefinite functionals. II: Bifurcation of periodic orbits of Hamiltonian systems ⋮ Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit ⋮ Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics ⋮ Trace formulas and the Conley-Zehnder index

Cites Work

• Der Indexsatz für geschlossene Geodätische
• Conjugacy classes in linear groups
• On the Morse index in variational calculus
• A generalized Sturm theorem
• Periodic geodesics on compact Riemannian manifolds
• On the iteration of closed geodesics and the sturm intersection theory

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