Symmetries and Reduction -- part I -- Poisson and symplectic picture

Abstract

Coherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem -- connecting symmetries with constants of the motion -- within a reduction. This is the first of two papers, and it focuses on the reduction within the Poisson and the symplectic formalism.

arXiv comment50 pages, revised version

References in corpus (13)

• Normal Forms, symmetry, and linearization of dynamical systems
• Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions
• Poisson structures on double Lie groups
• Schwinger's Picture of Quantum Mechanics I: Groupoids
• Schwinger's Picture of Quantum Mechanics III: The statistical interpretation
• Generalized Reduction Procedure: Symplectic and Poisson Formalism
• Schwinger's Picture of Quantum Mechanics II: Algebras and Observables
• Brackets
• Noncommutative differential calculus for Moyal subalgebras
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• Schwinger's Picture of Quantum Mechanics IV: Composition and independence
• Dynamical Aspects of Lie--Poisson Structures
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces

Cited by in corpus (3)

• Symmetries and Covariant Poisson brackets on pre-symplectic manifolds
• Symmetries and Reduction. Part II - Lagrangian and Hamilton-Jacobi picture
• Abstract Dynamical Systems: Remarks on Symmetries and Reduction