Perturbed Hamiltonian dynamics from deformation of Poisson brackets

DOI10.1134/S106192081903004XzbMath1468.70009OpenAlexW2971970143MaRDI QIDQ2334635

Yanyan Li

Publication date: 7 November 2019

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

Full work available at URL: https://doi.org/10.1134/s106192081903004x

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Topological and differential topological methods for problems in mechanics (70G40)

Cites Work

• On the global structure of normal forms for slow-fast Hamiltonian systems
• Homological equations for tensor fields and periodic averaging
• Poisson manifolds and the Schouten bracket
• Les variétés de Poisson et leurs algèbres de Lie associees
• Lectures on the geometry of Poisson manifolds
• Magneto-dimensional resonance. Pseudospin phase and hidden quantum number
• The Hannay angles: Geometry, adiabaticity, and an example
• Adiabatic approximation via hodograph translation and zero-curvature equations
• Adiabatics using phase space translations and small parameter ``dynamics
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• RELATIVISTIC CORRECTIONS TO ELEMENTARY GALILEAN DYNAMICS AND DEFORMATIONS OF POISSON BRACKETS
• Slow manifold and Hannay angle in the spinning top
• Reduction, symmetry, and phases in mechanics
• MOMENTUM MAPPINGS AND POISSON COHOMOLOGY
• Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems
• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems
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