The type numbers of closed geodesics

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Mors

Integrable Systems

Integrable systems which do not have an \u201cobvious\u201c group symmetry, beginning with the results of Poincar\ue9 and Bruns at the end of the last century, have been perceived as something exotic. The very insignificant list of such examples practically did not change until the 1960\u2019s. Although a number of fundamental methods of mathematical physics were based essentially on the perturbation-theory analysis of the simplest integrable examples, ideas about the structure of nontrivial integrable systems did not exert any real influence on the development of physics