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Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Differentiable dynamical systems. --- Differential equations, Hyperbolic. --- Dimension theory (Topology). --- Ergodic theory. --- Differentiable dynamical systems --- Ergodic theory --- Differential equations, Hyperbolic --- Dimension theory (Topology) --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Hyperbolic differential equations --- Ergodic transformations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Mathematics. --- Dynamics. --- Dynamical Systems and Ergodic Theory. --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Math --- Science --- Topology --- Differential equations, Partial --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.

Lyapunov exponents. --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Liapunov exponents --- Lyapunov characteristic exponents --- Mathematics. --- Dynamics. --- Ergodic theory. --- Dynamical Systems and Ergodic Theory. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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Ergodic theory. Information theory --- informatietheorie

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This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.

Differential geometry. Global analysis --- Ergodic theory. Information theory --- thermodynamica --- differentiaal geometrie --- informatietheorie

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This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can  be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.

Differential equations. --- Mathematical analysis. --- Mathematical analysis --- Differential equations --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Operations Research --- Applied Mathematics --- Fourier analysis. --- 517.91 Differential equations --- 517.1 Mathematical analysis --- Analysis, Fourier --- Mathematics. --- Functions of complex variables. --- Partial differential equations. --- Sequences (Mathematics). --- Fourier Analysis. --- Functions of a Complex Variable. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Sequences, Series, Summability. --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Partial differential equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Differential Equations. --- Differential equations, partial.