The Essence Of Chaos
CRC Press, 2 sep. 2003 - 227 pagina's
The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field.
Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals.
As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.
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CHAPTER 1 Glimpses of Chaos
CHAPTER 2 A Journey into Chaos
CHAPTER 3 Our Chaotic Weather
CHAPTER 4 Encounters with Chaos
CHAPTER 5 What Else Is Chaos?
APPENDIX 1 The Butterfly Effect
appear atmosphere ball basin become bifurcation butterfly Cantor set chaotic behavior close completely constant continually cross section curve Dave Fultz David Ruelle deterministic differential equations dimension dishpan dissipative system distance doubling dynamical systems equilibrium example extended Figure 12 fixed point flow fractal friction full chaos Hamiltonian systems happen horizontal horseshoe images infinite number initial intersect irregular look loops Lyapunov Lyapunov exponents manifold mapping mathematical mathematician meteorologists meters moguls motion move nonlinearity nonperiodic solutions numerical weather prediction observe occur original oscillations paths pendulum perhaps period-doubling bifurcations phase space pinball machine planets Poincarť mapping Poincarť section prediction primitive equations procedure produce random rectangle represent rotation segment sensitive dependence sequence set of points simple simulate ski slope sleds slide speed square stable manifold strange attractor stretching structure surface synoptic system of equations temperature unstable values variables vary velocity vertical weather forecasting weather patterns wind