Chaotic Dynamics and Transport in Classical and Quantum Systems: Proceedings of the NATO Advanced Study Institute on International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems, Cargèse, Corsica, 18 - 30 August 2003. (Google eBook)

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Pierre Collet
Springer Science & Business Media, Mar 30, 2006 - Chaotic behavior in systems - 469 pages
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This book offers a modern updated review on the most important activities in today dynamical systems and statistical mechanics by some of the best experts in the domain. It gives a contemporary and pedagogical view on theories of classical and quantum chaos and complexity in hamiltonian and ergodic systems and their applications to anomalous transport in fluids, plasmas, oceans and atom-optic devices and to control of chaotic transport. The book is issued from lecture notes of the International Summer School on 'Chaotic Dynamics and Transport in Classical and Quantum Systems' held in Cargèse (Corsica) 18th to the 30th August 2003. It reflects the spirit of the School to provide lectures at the post-doctoral level on basic concepts and tools. The first part concerns ergodicity and mixing, complexity and entropy functions, SRB measures, fractal dimensions and bifurcations in hamiltonian systems. Then, models of dynamical evolutions of transport processes in classical and quantum systems have been largely explained. The second part concerns transport in fluids, plasmas and reacting media. On the other hand, new experiments of cold optically trapped atoms and electrodynamics cavity have been thoroughly presented. Finally, several papers bear on synchronism and control of chaos. The target audience of the proceedings are physicists, mathematicians and all scientists involved in Chaos and Dynamical Systems Theory and their fundamental applications in Physics and in the Science of Complex and Nonlinear phenomena.
  

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Contents

A SHORT ERGODIC THEORY REFRESHER
1
NOTES ON SPECTRAL THEORY MIXING AND TRANSPORT
15
COMPLEXITY FRACTAL DIMENSIONS AND TOPOLOGICAL ENTROPY IN DYNAMICAL SYSTEMS
36
WORKING WITH COMPLEXITY FUNCTIONS
73
SRB distribution for Anosov maps
87
DYNAMICAL SYSTEMS THEORY OF IRREVERSIBILITY
106
ASPECTS OF OPEN QUANTUM SYSTEM DYNAMICS
159
ENERGY SURFACES AND HIERARCHIES OF BIFURCATIONS
188
FRACTAL TIME RANDOM WALK AND SUBRECOIL LASER COOLING CONSIDERED AS RENEWAL PROCESSES WITH INFINITE MEAN ...
281
ANOMALOUS TRANSPORT IN TWODIMENSIONAL PLASMA TURBULENCE
303
THE ONSET OF SYNCHRONISM IN GLOBALLYLL COUPLED ENSEMBLES OF CHAOTIC AND PERIODIC DYNAMICAL UNITS
320
QUANTUM BREAKING TIME FOR CHAOTIC SYSTEMS WITH PHASE SPACE STRUCTURES
333
HAMILTONIAN CHAOS AND FRACTALS IN CAVITY QUANTUM ELECTRODYNAMICS
349
INERT AND REACTING TRANSPORT
364
TRACER TRANSPORT DURING THE GEOSTROPHIC ADJUSTMENT IN THE EQUATORIAL OCEAN
413
THE FERMIPASTAULAM PROBLEM IN THE THERMODYNAMIC LIMIT
430

PhaseSpace Semiclassical Analysis Around Semiclassical Trace Formulae
225
ATOMOPTICS BILLIARDS
239
CONTROL OF CHAOS AND SEPARATION OF PARTICLES IN INERTIA RATCHETS
268
LECTURES
441
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