Part 1 Part 2 SIAM Talk

A recent review,closest to our point of view :

B. Khesin *Topological fluid dynamics*. Notices of the AMS, 52:1

(2005), 9-19

Similar textbook:

V. I. Arnold and B. Khesin *Topological Methods in
Hydrodynamics (Springer)
*

For basic knowledge of fluid mechanics:

L. D. Landau and Lifshitz *Fluid Mechanics* Pergamon Press.

Geophysics:

Rick Salmon *Lectures on Geophysical Fluid Dynamics*

J. Y. Chemin, B. Desjardins,I. Gallagher and E. Grenier

* Mathematical Geophysics *Oxford (2006)

Mathematical:

S. B. Kuskin *Randomly Forced NonLinear PDEs and Statistical Hydrodynamics in 2 Space Dimensions* European Math Soc. (2006).

this is the origin of the modern theory of elliptic curves.

The idea of approximating area preserving maps by matrices originates with J. Goldstone and his student J. Hoppe in the latter’s

Ph. D. Thesis (MIT 1983). See also

J. Hoppe Int. J. Mod. Phys. A4 5239 (1989);

There are many applications to hydrodynamics. As a sample,

R. J. MacLachlan Phys. Rev. Lett. 71 3043 (1993)

Rouhi, A., and H. D. I. Abarbanel Phys. Rev. E 48 (1993), 3643–3655

R. V. Abramov and A. J. Majda Proc. Nat. Sci. Acad USA {bf 100} 3841 (2003)

V. Zeitlin Phys Rev Lett 93 264501(2004)

The new conserved quantity for two dimensional Euler equations was discovered in Iyer,S. V. and Rajeev, S. G. Mod.Phys.Lett.A 17 1539 (2002)