The Foundations of Chaos Revisited From Poincar to Recent Advancements [Hardcover]

With contributions from a number of pioneeringresearchers in the field, this collection is aimed not only at researchers andscientists in nonlinear dynamics but also at a broader audience interested inunderstanding and exploring how modern chaos theory has developed since thedays of Poincar?.

 

This book was motivated by and isan outcome of the CHAOS 2015 meeting held at the Henri Poincar? Institute inParis, which provided a perfect opportunity to gain inspiration and discuss newperspectives on the history, development and modern aspects of chaos theory.

 

HenriPoincar? is remembered as a great mind in mathematics, physics and astronomy.His works, well beyond their rigorous mathematical and analytical style, areknown for their deep insights into science and research in general, and thephilosophy of science in particular. The Poincar? conjecture (only proved in2006) along with his work on the three-body problem are considered to be thefoundation of modern chaos theory.

Preface.- HenriPoincar?s inventions in dynamical systems and topology.- From nonlinearoscillations to chaos theory.- Hydrodynamic turbulence as a nonstandardtransport phenomenon.- Non-equilibrium statistical mechanics of turbulence: commentson Ruelle's intermittency theory.- The Kolmogorov law of turbulence  - what can rigorously be proved?.- History ofchaos from a French perspective.- Measuring quasiperiodicity.- Heat transfer ina complex medium.- Plasma hysteresis and instability: a memory perspective.- Stochasticanti-resonance in polarization phenomena.- A simple plankton model with complexbehavior.- Fractal Radar: Towards 1980  2015.- Simulation of multidimensionalnonlinear dynamics by one-dimensional maps with many parameters.- Suddencardiac death and turbulence.- Absolute negative mobility in a ratchet flow.

Christos Skiadas is the Founder andls>