On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

The Maximum Principle - how it came to be?

Formulations and discovery of the maximum principle are reviewed on the background of the latest Russian history. Dubovizki-Milyntin's method and the tents method are the most general tools for obtaining necessary criteria for various extremal problems. In this paper the tents method is preferred, since in the case, when Q_0 is a cone of admissible directions of #SIGMA#_0, and at the same time, it is not a tent of #SIGMA#_0, is pathological and rare. The convex cones separability theory has additional applications, e.g. it allows to establish new results in combinatorial geometry. (WEN)Available from TIB Hannover: RO 7722(526) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Tent method in optimal control theory

Available from TIB Hannover: RO 7722(308) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman