Counting spectrum via the Maslov index for one dimensional $\theta -$periodic Schrödinger operators

DOI10.1090/proc/13192zbMath1353.53080arXiv1510.05015OpenAlexW3104036695MaRDI QIDQ2832835

Selim Sukhtaiev, Yuri Latushkin, Christopher K. R. T. Jones

Publication date: 14 November 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.05015

zbMATH Keywords

stabilityeigenvaluesHamiltonian systemsSchrödinger equationdifferential operatorsdiscrete spectrum

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Lagrangian submanifolds; Maslov index (53D12) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

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Cites Work

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• Morse-Smale index theorems for elliptic boundary deformation problems
• Fredholm-Lagrangian-Grassmannian and the Maslov index
• Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space
• On the Morse index in variational calculus
• The Maslov index: A functional analytical definition and the spectral flow formula
• The Morse and Maslov indices for Schrödinger operators
• A Morse-Smale index theorem for indefinite elliptic systems and bifurcation
• Discrete and continuous boundary problems
• The Maslov and Morse indices for Schrödinger operators on \([0,1\)]
• The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials
• Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems
• On the iteration of closed geodesics and the sturm intersection theory
• Fast computation of the Maslov index for hyperbolic linear systems with periodic coefficients
• A Morse Index Theorem for Elliptic Operators on Bounded Domains
• Morse Theory. (AM-51)
• On the maslov index
• Manifold decompositions and indices of Schr\\\"{o}dinger operators
• The Spectral Flow and the Maslov Index
• Computing the Maslov index for large systems
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• The Morse and Maslov indices for matrix Hill's equations