Exceptional and diabolical points in stability questions

DOI10.1002/prop.201200068zbMath1338.81217OpenAlexW2070186718MaRDI QIDQ2812927

Oleg N. Kirillov

Publication date: 13 June 2016

Published in: Fortschritte der Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/prop.201200068

zbMATH Keywords

stabilitynon-conservative systemexceptional pointnon-Hermitian Hamiltonian

Mathematics Subject Classification ID

Hamilton's equations (70H05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (1)

A Coriolis force in an inertial frame

Cites Work

• On the dynamics of rotating and rolling structures
• Stability of equilibrium of a heavy particle on a rotating surface
• Quadratic matrix polynomials with Hamiltonian spectrum and oscillatory damped systems
• \({\mathcal PT}\)-symmetry, indefinite damping and dissipation-induced instabilities
• On destabilizing effects of two fundamental non-conservative forces
• Some general principles of dynamic instability of solid bodies
• Linear elastic stability. A critical analysis of methods
• About the stability of non-conservative undamped systems
• Sylvester’s eliminant and stability criteria for gyroscopic systems
• Quantal phase factors accompanying adiabatic changes
• A non-Hermitian Hamilton operator and the physics of open quantum systems
• Motion of a free particle on a beta-plane
• MULTIPLE EIGENVALUES AND MODE CLASSIFICATION IN PLANE OISEUILLE FLOW
• Standard forms of the eigenvalue problems associated with gyroscopic systems
• Energy, dynamics, hidden machinery: Rankine, Thomson and Tait, Maxwell
• On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure
• Eigencurves for Two-Parameter Sturm-Liouville Equations
• The role of damping in vibration theory
• ON MATRICES DEPENDING ON PARAMETERS
• Rotating class of parametric resonance processes in coupled oscillators
• The mechanics of inertial motion on the Earth and on a rotating sphere

This page was built for publication: Exceptional and diabolical points in stability questions