Advances in Discrete Dynamics

Discrete dynamical systems, the main topic of this book, have had a fast development due to the development of computer science. Programming an iteration with the form xn+1 = f(xn), where f is a real function is made easy with modern computers. So, with the modern computer, it is relatively easy and fast to obtain simulations related with the dynamics of their models.

Finding analytical proofs for computer simulations of models are natural and exciting problems for mathematicians and, like in a feedback process, new powerful analytical results motivate the use of discrete models. This new book examines the theory of dynamical systems. (Imprint: Nova)

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Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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Discrete dynamical systems, the main topic of this book, have had a fast development due to the development of computer science. Programming an iteration with the form xn+1 = f(xn), where f is a real function is made easy with modern computers. So, with the modern computer, it is relatively easy and fast to obtain simulations related with the dynamics of their models. Finding analytical proofs for computer simulations of models are natural and exciting problems for mathematicians and, like in a feedback process, new powerful analytical results motivate the use of discrete models. This new book examines the theory of dynamical systems. (Imprint: Nova)

Preface pp.vii-viii

Chapter 1. Periodic Structure of Discrete Dynamical Systems
and Global Periodicity
(Antonio Linero) pp.1-64

Chapter 2. Shadowing Techniques and Chaotic Phenomena
(Rongbao Gu) pp.65-90

Chapter 3. W-limit Sets of Discrete-Time Dynamical Systems
(Emma D’Aniello) pp91-114

Chapter 4. Topological Entropy in one Dimensional Dynamics
(Jose S. C´anovas) pp.115-154

Chapter 5. Transitive and Minimal Flows and Interval
Exchange Transformations
(Gabriel Soler L´opez)pp.155-182

Chapter 6. Entropy and Complexity in Dynamical Systems and PDEs
(Claudio Bonanno)pp.183-218

Chapter 7. On Cournot–Puu Duopoly
(Jose S. C´anovas)pp.219-252

Chapter 8. Testing Causality in Time Series
(Mariano Matilla Garc´ýa & Manuel Ruiz Mar´ýn) pp.253-272

Index pp.273-277

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