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Spectral theory and asymptotics of differential equations

Differential equations --- Spectral theory (Mathematics) --- Asymptotic theory --- Équations différentielles. --- Théorie spectrale (mathématiques) --- Differential equations. --- Equations differentielles ordinaires --- Developpements asymptotiques

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This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.

Differentiable dynamical systems. --- Electronic books. -- local. --- Point mappings (Mathematics). --- Differentiable dynamical systems --- Point mappings (Mathematics) --- Spectral theory (Mathematics) --- Mathematics --- Geometry --- Calculus --- Physical Sciences & Mathematics --- Equations, Recurrent --- Mappings, Point (Mathematics) --- Recurrence relations in functional differential equations --- Recurrent equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Dynamics. --- Ergodic theory. --- Fourier analysis. --- Measure theory. --- Operator theory. --- Number theory. --- Analysis. --- Dynamical Systems and Ergodic Theory. --- Fourier Analysis. --- Number Theory. --- Measure and Integration. --- Operator Theory. --- Number study --- Numbers, Theory of --- Algebra --- Functional analysis --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Analysis, Fourier --- Mathematical analysis --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- 517.1 Mathematical analysis --- Math --- Science --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Functional differential equations --- Mappings (Mathematics) --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Dynamique différentiable --- Applications ponctuelles (mathématiques) --- Théorie spectrale (mathématiques) --- Hilbert space --- Dynamique différentiable --- Applications ponctuelles (mathématiques) --- Théorie spectrale (mathématiques)