symplectic geometry
Symplectic geometry is a branch of mathematics that studies geometric properties arising from the symplectic structure, a mathematical structure defined on certain spaces called symplectic manifolds. It focuses on the study of symplectic maps, which preserve the symplectic structure, and symplectic transformations, which preserve the geometric structure and symmetries of a symplectic manifold.
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Related Concepts (22)
- arnold-liouville theorem
- classical mechanics
- contact geometry
- darboux theorem
- deformation quantization
- floer homology
- gromov-witten invariants
- hamilton-jacobi theory
- hamiltonian systems
- integrable systems
- lagrangian mechanics
- moment maps
- phase space
- poincaré maps
- poisson geometry
- quantum symplectic geometry
- symplectic capacity
- symplectic embeddings
- symplectic groupoids
- symplectic manifolds
- symplectic reduction
- symplectic topology