By G. R. Belitsky, and E. V. Zhuzhoma S. Kh. Aranson
This publication is an creation to the qualitative idea of dynamical structures on manifolds of low size (on the circle and on surfaces). besides classical effects, it displays the main major achievements during this quarter received in recent years by way of Russian and international mathematicians whose paintings has no longer but seemed within the monographic literature. the most rigidity here's wear worldwide difficulties within the qualitative idea of flows on surfaces.
Despite the truth that flows on surfaces have an analogous neighborhood constitution as flows at the aircraft, they've got many international homes intrinsic to multidimensional platforms. this is often attached regularly with the lifestyles of nontrivial recurrent trajectories for such flows. The research of dynamical structures on surfaces is as a result a common degree within the transition to multidimensional dynamical systems.
The reader of this e-book desire be ordinary simply with simple classes in differential equations and gentle manifolds. all of the major definitions and ideas required for realizing the contents are given within the text.
The effects expounded can be utilized for investigating mathematical types of mechanical, actual, and different structures (billiards in polygons, the dynamics of a spinning best with nonholonomic constraints, the constitution of liquid crystals, etc.).
In our opinion the ebook can be priceless not just to mathematicians in all parts, but in addition to experts with a mathematical history who're learning dynamical methods: mechanical engineers, physicists, biologists, and so on.
Readership: Graduate scholars and researchers operating in dynamical structures and differential equations, in addition to experts with a mathematical heritage who're learning dynamical procedures: mechanical engineers, physicists, biologists, and so forth.