This volume offers an account of the present state of the art in pseudoperiodic topology--a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience.

From the Preface by V.I. Arnold: "The authors ... have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting."

Readership

Graduate students and research mathematicians interested in geometry and topology, specifically differential topology.

Table of Contents

• S. M. Gusein-Zade -- On the topology of quasiperiodic functions
• M. L. Kontsevich and Yu. M. Suhov -- Statistics of Klein polyhedra and multidimensional continued fractions
• A. Pajitnov -- \(C^0\)-generic properties of boundary operators in the Novikov complex
• D. A. Panov -- Pseudoperiodic mappings
• A. Zorich -- How do the leaves of a closed 1-form wind around a surface?