Simultaneous local normal forms of dynamical systems with singular underlying geometric structures
DOI10.1088/1361-6544/ad700dMaRDI QIDQ6608796
Tudor S. Ratiu, Nguyen Tien Zung, Kai Jiang
Publication date: 20 September 2024
Published in: Nonlinearity (Search for Journal in Brave)
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Differential forms in global analysis (58A10) Exterior differential systems (Cartan theory) (58A15) 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)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Symplectic and Poisson geometry on \( b\)-manifolds
- Integrability of dynamical systems: algebra and analysis
- The normal form theorem around Poisson transversals
- The tropical momentum map: a classification of toric log symplectic manifolds
- The local structure of Poisson manifolds
- Convergence versus integrability in Poincaré-Dulac normal form
- A conceptual approach to the problem of action-angle variables
- A note on equivariant normal forms of Poisson structures
- Normal forms of vector fields on Poisson manifolds
- Singularités d'ordre supérieur de 1-formes, 2-formes et équations de Pfaff
- Equivalence of glancing hypersurfaces. II
- Manifolds, tensor analysis, and applications.
- On differential equations in normal form
- Convergence of Birkhoff normal forms for integrable systems
- On the Poincaré problem
- Equivariant Sternberg-Chen theorem
- Classification of \(b^m\)-Nambu structures of top degree
- Logarithmic differential forms on varieties with singularities
- Equivariant classification of \(b^m\)-symplectic surfaces
- A new family of nondegenerate Lie algebras
- The geometry of \(E\)-manifolds
- Invariant ideals of local analytic and formal vector fields
- Relative logarithmic cohomology and Nambu structures of maximal degree
- On the volume elements of a manifold with transverse zeroes
- Convergence versus integrability in Birkhoff normal form
- Sur les singularités des formes différentielles
- Equations différentielles à points singuliers réguliers
- Poisson structures and their normal forms
- Local Darboux first integrals of analytic differential systems
- Compact groups of differentiable transformations
- Symplectic Groupoids of Log Symplectic Manifolds
- Geometry of Integrable non-Hamiltonian Systems
- Algèbres commutatives de champs de vecteurs isochores
- On the Volume Elements on a Manifold
- Remarks on a Paper of Hermann
- Dynamical systems
- Local reduction theorems and invariants for singular contact structures.
- Singular complete integrability
- Normalization of singular contact forms and primitive 1-forms
This page was built for publication: Simultaneous local normal forms of dynamical systems with singular underlying geometric structures
