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This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps). Various classes of minimal flows (equicontinuous, distal, point distal) are intensively studied, and a general structure theorem is obtained. Another theme is the ``universal'' approach - entire classes of minimal flows are studied, rather than flows in isolation. This leads to the consideration of disjointness of flows,

Minimal flows. --- Topological dynamics. --- Dynamics, Topological --- Differentiable dynamical systems --- Flows (Differentiable dynamical systems)

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Differential geometry. Global analysis --- Flows (Differentiable dynamical systems) --- Flows (Differentieerbare systemen) --- Flows (Systèmes dynamiques différentiables) --- Hamiltonian systems --- Hamiltonsystemen --- Perturbatie (Wiskunde) --- Perturbation (Mathematics) --- Perturbation (Mathématiques) --- Systèmes hamiltoniens --- Tore (Geometrie) --- Torus (Geometry) --- Torus (Meetkunde) --- Hamiltonian systems. --- Flows (Differentiable dynamical systems). --- Perturbation (Mathematics). --- Torus (Geometry).

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This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 100 papers, and his research has played an important role in the development of the theory and applications of monotone dynamical systems, periodic and almost periodic semiflows, uniform persistence, and basic reproduction ratios.

Mathematics. --- Dynamics. --- Ergodic theory. --- Biomathematics. --- Dynamical Systems and Ergodic Theory. --- Mathematics of Planet Earth. --- Genetics and Population Dynamics. --- Population biology --- Flows (Differentiable dynamical systems) --- Mathematical models. --- Differentiable dynamical systems --- Differentiable dynamical systems. --- Genetics --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Math --- Science --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Mathematics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics