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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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Dynamical systems is an area of intense research activity and one which finds application in many other areas of mathematics. This volume comprises a collection of survey articles that review several different areas of research. Each paper is intended to provide both an overview of a specific area and an introduction to new ideas and techniques. The authors have been encouraged to include a selection of open questions as a spur to further research. Topics covered include global bifurcations in chaotic o.d.e.s, knotted orbits in differential equations, bifurcations with symmetry, renormalization and universality, and one-dimensional dynamics. Articles include comprehensive lists of references to the research literature and consequently the volume will provide an excellent guide to dynamical systems research for graduate students coming to the subject and for research mathematicians.

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

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Differentiable dynamical systems --- Hamiltonian systems --- Classical mechanics. Field theory --- Differentiable dynamical systems. --- Hamiltonian systems. --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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Differential geometry. Global analysis --- Differentiable dynamical systems --- Vector fields --- Symmetry --- Direction fields (Mathematics) --- Fields, Direction (Mathematics) --- Fields, Slope (Mathematics) --- Fields, Vector --- Slope fields (Mathematics) --- Vector analysis --- Aesthetics --- Proportion --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differentiable dynamical systems. --- Symmetry. --- Vector fields. --- Géometrie différentielle --- Mécanique analytique --- Systèmes dynamiques

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Differential geometry. Global analysis --- Differentiable dynamical systems --- Dynamique différentiable --- Differentiable dynamical systems. --- #TELE:SISTA --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamique différentiable --- Systèmes dynamiques. --- Dynamique différentiable. --- Systèmes dynamiques. --- Dynamique différentiable.