Geometry, dynamics and different types of orbits

DOI10.1007/s11784-014-0189-9zbMath1346.17007OpenAlexW2332443672WikidataQ125807377 ScholiaQ125807377MaRDI QIDQ490041

A. T. Fomenko, Andrey Yu. Konyaev

Publication date: 21 January 2015

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-014-0189-9

zbMATH Keywords

Lie algebracoadjoint obitsdynamical systems, Bertrand manifolds

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Coadjoint orbits; nilpotent varieties (17B08)

Cites Work

• The global and local realizability of Bertrand Riemannian manifolds as surfaces of revolution
• The explicit form of the Bertrand metric
• New approach to symmetries and singularities in integrable Hamiltonian systems
• The integrability of some Hamiltonian systems
• Morse-type theory for integrable Hamiltonian systems with tame integrals
• Taut representations of compact simple Lie groups
• Cycles of Bott-Samelson type for taut representations
• Lie groups whose coadjoint orbits are of dimension smaller or equal to two
• Symmetries groups of nice Morse functions on surfaces
• Minimal linear Morse functions on the orbits in Lie algebras
• Application of Morse theory to some homogeneous spaces
• The product of the generators of a finite group generated by reflections
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• Commutative homogeneous spaces with one-dimensional stabilizer
• Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation
• Applications of the Theory of Morse to Symmetric Spaces
• Liouville integrability of Hamiltonian systems on Lie algebras
• THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS
• Invariants of real low dimension Lie algebras
• A generalization of Bertrand's theorem to surfaces of revolution
• The classification of taut irreducible representations
• Gravitational and harmonic oscillator potentials on surfaces of revolution
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