The Top Theory

In the age of adventure, when dirigibles coasted through the air and vast swaths of the Earth remained untouched and unseen by man, one pack of relentless explorers competed in the race of a lifetime: to be the first aviator to fly over the North Pole. What inspired their dangerous fascination? For some, it was the romantic theory about a “lost world,” a hidden continent in the Arctic Ocean.

This book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achievements in this area obtained in recent times by Russian and foreign mathematicians whose work has not yet appeared in the monographic literature.