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Differentiable dynamical systems --- Equations, Quadratic --- Newton-Raphson method

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Differentiable dynamical systems --- Differential equations --- Dynamique différentiable --- Equations différentielles

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We are living in an ever more complex world, an epoch where human actions can accordingly acquire far-reaching potentialities. Complex and adaptive dynamical systems are ubiquitous in the world surrounding us and require us to adapt to new realities and the way of dealing with them. This primer has been developed with the aim of conveying a wide range of "commons-sense" knowledge in the field of quantitative complex system science at an introductory level, providing an entry point to this both fascinating and vitally important subject. The approach is modular and phenomenology driven. Examples of emerging phenomena of generic importance treated in this book are: -- The small world phenomenon in social and scale-free networks. -- Phase transitions and self-organized criticality in adaptive systems. -- Life at the edge of chaos and coevolutionary avalanches resulting from the unfolding of all living. -- The concept of living dynamical systems and emotional diffusive control within cognitive system theory. Technical course prerequisites are a basic knowledge of ordinary and partial differential equations and of statistics. Each chapter comes with exercises and suggestions for further reading - solutions to the exercises are also provided.

Mathematics --- Statistical physics --- General biophysics --- Computer science --- Information systems --- ICT (informatie- en communicatietechnieken) --- biofysica --- toegepaste wiskunde --- informatica --- statistiek --- informatiesystemen --- fysica --- Adaptive control systems. --- Differentiable dynamical systems.

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After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many others to take up this increasingly active subject, and will continue to do so. Presenting papers by researchers in transcendental dynamics and complex analysis, this book is written in honour of Noel Baker. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading for students and researchers in complex dynamics and complex analysis.

Functions of complex variables. --- Differentiable dynamical systems. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Complex variables --- Elliptic functions --- Functions of real variables

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Presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems.

Dynamics. --- Nonlinear systems. --- Chaotic behavior in systems. --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Systems, Nonlinear --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics