Abstract
Symplectic geometry is the mathematical apparatus of such areas of physics as classical mechanics, geometrical optics and thermodynamics. Whenever the equations of a theory can be gotten out of a variational principle, symplectic geometry clears up and systematizes the relations between the quantities entering into the theory. Symplectic geometry simplifies and makes perceptible the frightening formal apparatus of Hamiltonian dynamics and the calculus of variations in the same way that the ordinary geometry of linear spaces reduces cumbersome coordinate computations to a small number of simple basic principles.
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Added in proof: Additional list of new publications On linear symplectic geometry:
Arnol’d V.I.: The Sturm theorems und symplectic geometry. Funkts. Anal. Prilozh. 19, No. 4, 1–10 (1985) (English translation: Funct. Anal. Appl. 19, 251–259 (1985))
On Poisson structures:
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Arnol’d, V.I.: On the interior scattering of waves defined by the hyperbolic variational principles. To appear in J. Geom. Phys. 6 (1989)
On geometrical optics:
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On cobordism theory:
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On Lagrangian intersections:
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Arnol’d, V.I., Givental’, A.B. (1990). Symplectic Geometry. In: Arnol’d, V.I., Novikov, S.P. (eds) Dynamical Systems IV. Encyclopaedia of Mathematical Sciences, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06793-2_1
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