By Laberto Cesari, Jack. K. Hale, Joseph P. LaSalle

Lawsuits of a world Symposium on Dynamical platforms held at Brown college, August 12-16, 1974

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Structural stability and the Störmer problem Ind. Univ. Math. J. 20 (1970), 469-497. , Some recent results for the Störmer problem (in preparation). , Some theoretical and numerical results of an area preserving mapping (in preparation). [7] J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. , Göttingen: Math. Phys. Kl. lia (1) (1962), 1-20. A Geometrical Approach to Classical Mechanics CHONG-PIN ONGt Department of Mathematics University of California, Berkeley, California 1 .

Due to the individual ergodic theorem we have V = lim- iv(sk)=\i V(shf(ds). (22) So, knowing the invariant measure, we are able to count the mean efficiency per blow. In a similar way, it is possible to find a mean expenditure per blow. The received formulas appear to be in accordance with drilling practice (see [4]). They can also be useful for optimizing drilling tool efficiency. Our second example is connected with the technology of foundry casting. After cooling, the molds must be cleaned of sand, clay, and other materials sticking to them.

R. Acad. Sei. Paris, Sér. A-B 266 (1968), A610-A612. MR 37 No. 6944. [2] C. Foias, Statistical study of Navier-Stokes equation II, Rend. Sem. Mat. Univ. Padova 49 (1973), 9-123. [3] K. Krzyzewski and W. Szlenk, On invariant measures for expanding differentiable mappings, Stud. Math. 33 (1969), 83-92. MR 39 No. 7067. [4] A. Lasota and P. Rusek, An application of ergodic theory to the determination of the efficiency of cogged drilling bits (Polish with Russian and English summaries). Arch. Gornictwa 19 (1974), 281-295.