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From Dynamics to Contact and Symplectic Topology and Back
TL;DR: In this article, a light survey article about the origins of contact and symplectic topology in dynamics and the more recent developments in the field is presented, where numerous anecdotes are given.
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Abstract: This is a light survey article about the origins of contact and symplectic topology in dynamics and the more recent developments in the field. In lieu of formulas, numerous anecdotes are given.
read more
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Mathematical Methods of Classical Mechanics
Vladimir I. Arnold
- 01 Jan 1974
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
12.5K
Mathematical methods of classical mechanics
Vladimir I. Arnold
- 01 Jan 1978
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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Pseudo holomorphic curves in symplectic manifolds
TL;DR: In this article, the authors define a parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J).
2.7K
The classical groups : their invariants and representations
Hermann Weyl
- 31 Jan 1947
TL;DR: Weyl as discussed by the authors discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations using basic concepts from algebra, and examines the various properties of the groups.
2.4K
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Introduction to symplectic topology
Dusa McDuff,Dietmar Salamon +1 more
- 01 Jan 1995
TL;DR: In this article, the authors present a survey of the history of classical and modern manifold geometry, from classical to modern, including linear and almost complex structures, and the Arnold conjecture of the group of symplectomorphisms.
2K
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