Ebook: 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.

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There has been a growing interaction between the mathematical study of real dynamical systems and complex dynamical systems. Problems in the real dynamical system area have been solved by 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 the real area. The present volume examines the state of the art of central parts of both real and complex dynamical systems, reinforcing contact between the two aspects of the theory, making recent progress in each accessible to a larger group of mathematicians.

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There has been a growing interaction between the mathematical study of real dynamical systems and complex dynamical systems. Problems in the real dynamical system area have been solved by 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 the real area. The present volume examines the state of the art of central parts of both real and complex dynamical systems, reinforcing contact between the two aspects of the theory, making recent progress in each accessible to a larger group of mathematicians.

Content:
Front Matter....Pages i-xvii
Dynamical Zeta Functions....Pages 1-26
The Global Dynamics of Impact Oscillators....Pages 27-46
Grazing in Impact Oscillators....Pages 47-63
Topological Entropy of Unimodal Maps....Pages 65-87
H?non Mappings in the Complex Domain....Pages 89-132
Symbolic Dynamics, Group Automorphisms and Markov Partitions....Pages 133-163
A Monotonicity Conjecture for Real Cubic Maps....Pages 165-183
Dynamics of Ordinary Differential Equations....Pages 185-210
Real Bounds in Complex Dynamics....Pages 211-229
Homoclinic Bifurcations and Strange Attractors....Pages 231-264
Introduction to Hyperbolic Dynamics....Pages 265-291
Ergodic Theory of Differentiable Dynamical Systems....Pages 293-336
Back Matter....Pages 337-344

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There has been a growing interaction between the mathematical study of real dynamical systems and complex dynamical systems. Problems in the real dynamical system area have been solved by 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 the real area. The present volume examines the state of the art of central parts of both real and complex dynamical systems, reinforcing contact between the two aspects of the theory, making recent progress in each accessible to a larger group of mathematicians.

Content:
Front Matter....Pages i-xvii
Dynamical Zeta Functions....Pages 1-26
The Global Dynamics of Impact Oscillators....Pages 27-46
Grazing in Impact Oscillators....Pages 47-63
Topological Entropy of Unimodal Maps....Pages 65-87
H?non Mappings in the Complex Domain....Pages 89-132
Symbolic Dynamics, Group Automorphisms and Markov Partitions....Pages 133-163
A Monotonicity Conjecture for Real Cubic Maps....Pages 165-183
Dynamics of Ordinary Differential Equations....Pages 185-210
Real Bounds in Complex Dynamics....Pages 211-229
Homoclinic Bifurcations and Strange Attractors....Pages 231-264
Introduction to Hyperbolic Dynamics....Pages 265-291
Ergodic Theory of Differentiable Dynamical Systems....Pages 293-336
Back Matter....Pages 337-344
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