Structurally stable nondegenerate singularities of integrable systems

DOI10.1134/S106192082201006XzbMath1495.37047arXiv2112.00130OpenAlexW3215677978MaRDI QIDQ2120149

E. A. Kudryavtseva, A. A. Oshemkov

Publication date: 31 March 2022

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.00130

zbMATH Keywords

Kovalevskaya topLagrangian fibrationcompletely integrable system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Perturbation methods for rigid body dynamics (70E20) Integrable cases of motion in rigid body dynamics (70E40) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (1)

Classification of singularities of smooth functions with a finite cyclic symmetry group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Smooth normal forms for integrable Hamiltonian systems near a focus-focus singularity
• Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems
• Singularities of integrable and near-integrable Hamiltonian systems
• Convergence versus integrability in Poincaré-Dulac normal form
• Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
• Topological invariants of Liouville integrable Hamiltonian systems
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Mapping of periods and intersection form
• Bifurcation of common levels of first integrals of the Kovalevskaya problem
• The Hamiltonian Hopf bifurcation
• Le lemme de Morse isochore
• A normally elliptic Hamiltonian bifurcation
• Actions toriques et groupes d'automorphismes de singularités des systèmes dynamiques intégrables. (Torus actions and automorphism groups of singularities of integrable dynamical systems)
• A note on degenerate corank-one singularities of integrable Hamiltonian systems
• Integrable systems with linear periodic integral for the Lie algebra e(3)
• An analogue of the Liouville theorem for integrable Hamiltonian systems with incomplete flows
• Action-angle coordinates at singularities for analytic integrable systems
• On semi-global invariants for focus-focus singularities
• Isoenergetic classification of integrable Hamiltonian systems in a neighborhood of a simple elliptic point
• Decomposition of nondegenerate singularities of integrable Hamiltonian systems
• Existence of a smooth Hamiltonian circle action near parabolic orbits and cuspidal tori
• Hidden toric symmetry and structural stability of singularities in integrable systems
• Smooth invariants of focus-focus singularities and obstructions to product decomposition
• Convergence versus integrability in Birkhoff normal form
• Saddle singularities of complexity 1 of integrable Hamiltonian systems
• The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian
• Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems
• Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems
• Classification of almost toric singularities of Lagrangian foliations
• Sur Certains Systemes Dynamiques Separables
• Typical integrable Hamiltonian systems on a four-dimensional symplectic manifold
• CLASSIFICATION OF FOUR-DIMENSIONAL INTEGRABLE HAMILTONIAN SYSTEMS AND POISSON ACTIONS OF $ \mathbb{R}^2$ IN EXTENDED NEIGHBORHOODS OF SIMPLE SINGULAR POINTS. I
• Integrable Hamiltonian system with two degrees of freedom. The topological structure of saturated neighbourhoods of points of focus-focus and saddle-saddle type
• The method of loop molecules and the topology of the Kovalevskaya top
• Symplectic invariants for parabolic orbits and cusp singularities of integrable systems
• Integrable perturbations of saddle singularities of rank 0 of integrable Hamiltonian systems
• The topology associated with cusp singular points

This page was built for publication: Structurally stable nondegenerate singularities of integrable systems