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Timeevolution in lowdimensional topological spaces is a subject of puzzling vitality. This book is a stateoftheart account, covering classical and new results. The volume comprises PoincarBendixson, local and MorseSmale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the AnosovWeil problem, C*algebras and noncompact surfaces. The book invites graduate students and nonspecialists to a fascinating realm of research. It is a valuable source of reference to the specialists
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