Real and Complex Dynamical Systems

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex Dynamical Systems have been settled using results from Real Dynamical Systems. The programme of the institute was to examine the state of the art of central parts of both Real and Complex Dynamical Systems, to reinforce contact between the two aspects of the theory and to make recent progress in each accessible to a larger group of mathematicians.

Dynamical Zeta Functions.- The Global Dynamics of Impact Oscillators.- Grazing in Impact Oscillators.- Topological Entropy of Unimodal Maps.- Hénon Mappings in the Complex Domain.- Symbolic Dynamics, Group Automorphisms and Markov Partitions.- A Monotonicity Conjecture for Real Cubic Maps.- Dynamics of Ordinary Differential Equations.- Real Bounds in Complex Dynamics.- Homoclinic Bifurcations and Strange Attractors.- to Hyperbolic Dynamics.- Ergodic Theory of Differentiable Dynamical Systems.