Fixed point theorems and their applications (Q2842210)

The book begins with the classical Brouwer fixed point theorem, which leads to the Schauder-Tychonoff fixed point theorem in analysis and to the Lefschetz fixed point theorem in topology, with some applications. Next, it deals with fixed point theorems in geometry, including Cartan's theorem on compact groups of isometries of Hadamard manifolds and with Borel's fixed point theorem in algebraic groups. Moreover, concerning fixed points of volume preserving maps, which are of great importance in dynamical systems, the Poincaré recurrence theorem, Arnold's conjecture, Poincaré's last geometric theorem, Anosov diffeomorphisms, and the Lefschetz zeta function are treated. Last but not least, some connections of fixed points to number theory, group theory, complex analysis and even set theory are briefly described.NEWLINENEWLINEThis book provides a rich source of information on fixed point theorems in various branches of mathematics.