The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

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Christos Skiadas
Springer, Apr 29, 2016 - Science - 261 pages

With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré.

This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory.

Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.

 

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Contents

1 Henri Poincarés Inventions in Dynamical Systems and Topology
1
2 From Nonlinear Oscillations to Chaos Theory
27
3 Hydrodynamic Turbulence as a Nonstandard Transport Phenomenon
48
4 Nonequilibrium Statistical Mechanics of Turbulence
59
5 The Kolmogorov Law of Turbulence What Can Rigorously Be Proved? Part II
71
6 History of Chaos from a French Perspective
90
Rotation Numbers
103
8 Heat Transfer in a Complex Medium
119
A Memory Perspective
137
10 Stochastic AntiResonance in Polarization Phenomena
158
11 A Simple Plankton Model with Complex Behaviour
181
A Look from 2015
195
13 Simulation of Multidimensional Nonlinear Dynamics by OneDimensional Maps with Many Parameters
219
14 Sudden Cardiac Death and Turbulence
234
15 Absolute Negative Mobility in a Ratchet Flow
249
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About the author (2016)

Christos Skiadas is the Founder and Director of the Data Analysis and Forecasting Laboratory in the Technical University of Crete. A former vice-Rector of the Technical University of Crete and Chairman of the Department of Production Engineering and Management, he also served as a consultant in various firms. His main scientific and research interests is innovation diffusion modelling and forecasting, life table data modelling and healthy life expectancy estimates, including applications in finance and insurance. He conducts also research in deterministic, stochastic and chaotic modeling. Among the many books he has authored and edited is the article collection Advances in Data Analysis (Springer Birkhäuser Basel 2010).

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