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“…Thirty-two participants saw three fractals as CSs (CS(+)1, CS(+)2, CS(−)) and received electric shocks as USs. …”
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“…Their potential use in modern art was demonstrated by drying silver colloids on different surfaces in the presence of reagents or purified, resulting in a variety of colors but, more importantly, patterns of varying complexity, from simple multi-coffee-rings structures to dendritic forms and complex multilevel Sierpiński triangle fractals.…”
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“…This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapter 9 discusses the quantum mechanics of systems driven by time-periodic forces Chapter 10 reviews some recent work on the stochastic manifestations of chaos The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature End of chapter problems help students clarify their understanding In this new edition, the presentation has been brought up to date throughout, and a new chapter on open quantum systems has been added About the author Linda E Reichl, PhD, is a Professor of Physics at the University of Texas at Austin and has served as Acting Director of the Ilya Prigogine Center for Statistical Mechanics and Complex Systems since 1974 She is a Fellow of the American Physical Society and currently is US Editor of the journal Chaos, Solitons, and Fractals…”
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“…The book contains graphical renderings of many of the mathematical objects the authors discuss, including some of the intriguing fractals Fatou and Julia studied, and concludes with several appendices by current researchers in complex dynamics which collectively attest to the impact of the work of Fatou, Julia, and others upon the present-day study.…”
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“…Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. …”
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