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Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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This book provides an introduction to discrete dynamical systems -- a framework of analysis commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. The book characterizes the fundamental factors that govern the qualitative and quantitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors the govern the evolution of state variables in the elementary context of one-dimensional, first-order, linear, autonomous systems. The fundamental insights about the forces that affect the evolution of these elementary systems are subsequently generalized, and the determinants of the trajectory of multi-dimensional, nonlinear, higher-order, non-autonomous dynamical systems are established.

Differentiable dynamical systems. --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Differentiable dynamical systems

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Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures - recurrent patterns - in turbulent flows, it describes mathematical methods that reduce the governing (Navier-Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge.

Differentiable dynamical systems. --- SCIENCE / Physics. --- Turbulence. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics

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The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They succinctly cover an unparalleled range of topics from the basic concepts of symplectic and Poisson geometry, through integrable systems, KAM theory, fluid dynamics, and symmetric bifurcation theory. The lectures are based on summer schools for graduate students and postdocs and provide complementary and contrasting viewpoints of key topics: the authors cut through an overwhelming amount of literature to show young mathematicians how to get to the core of the various subjects and thereby enable them to embark on research careers.

Mechanics, Analytic. --- Geometry, Differential. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differential geometry --- Analytical mechanics --- Kinetics

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"Computational Methods for Nonlinear Dynamical Systems proposes novel ideas and develops highly efficient and accurate methods for solving nonlinear dynamical systems, drawing inspiration from the weighted residual method and the asymptomatic method. The book also introduces global estimation methods and local computational methods for nonlinear dynamical systems. Starting from the classic asymptomatic, finite difference and weighted residual methods, typical methods for solving nonlinear dynamical systems are considered. All proposed are new high-performance methods, such as time-domain collocation and local variational iteration. These proposed methods can be used both for real-time simulation and for the analysis of nonlinear dynamics in aerospace engineering. This book summarizes and develops computational methods for strongly nonlinear dynamical systems and considers the practical application of the methods within aerospace engineering, making it an essential resource for those working in this area."--

Aerospace engineering --- Differentiable dynamical systems. --- Nonlinear systems. --- Systems, Nonlinear --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics