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This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

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

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By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents:PrefaceMathematical symbolsNumber-theoretical dynamical systemsBasic ergodic theoryRenewal theory and α-sum-level setsInfinite ergodic theoryApplications of infinite ergodic theoryBibliographyIndex

Ergodic theory. --- Topological dynamics. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics, Topological --- Differentiable dynamical systems --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamique différentiable. --- Théorie ergodique. --- Dynamique topologique. --- Dynamique différentiable. --- Théorie ergodique.

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Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.

Mathematics. --- Algebra. --- Field theory (Physics). --- Dynamics. --- Ergodic theory. --- Differential geometry. --- Dynamical Systems and Ergodic Theory. --- Differential Geometry. --- Field Theory and Polynomials. --- Differential geometry --- Ergodic transformations --- Dynamical systems --- Kinetics --- Classical field theory --- Continuum physics --- Math --- Differentiable dynamical systems. --- Global differential geometry. --- Physics --- Continuum mechanics --- Geometry, Differential --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Geometry, Algebraic. --- Mathematics --- Mathematical analysis --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics

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The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- Lyapunov exponents. --- Cocycles. --- Grassmann manifolds. --- Grassmannians --- Liapunov exponents --- Lyapunov characteristic exponents --- Differential topology --- Manifolds (Mathematics) --- Algebra, Homological --- Differential equations --- Differentiable dynamical systems. --- Dynamical Systems and Ergodic Theory. --- Mathematical Physics. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- Mathematical physics. --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics

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This book explores how to design and implement planning & control (P&C) systems that can help organizations to manage their growth and restructuring processes in a sustainability perspective. The book is not designed to enable the reader to become an experienced system dynamics modeler; rather, it aims to develop the reader’s capabilities to design and implement performance management systems by using a system dynamics approach. More specifically, the book shows how to develop system dynamics models that can better support an understanding of: -What is organizational performance and how to frame and measure it; -How to identify and map the processes underlying performance; -How to design and implement a dynamic performance management system and link it to strategic planning; -How to tie strategic resource dynamics to processes and performance indicators; -How to link strategic resources, and performance indicators to responsibility and incentive systems. e:AR-SA">Using a dynamic performance management approach can improve an organization’s capability to understand and manage the forces driving performance over time, as well as set goals and objectives that may properly and selectively gauge results and match them to the key responsibility areas in the planning process. The dynamic performance management approaches covered in the book are beneficial to performance management analysts, enabling them to frame their professional field within the broader context of the system. The book also includes numerous case studies and dynamic performance management models for providing examples of how dynamic performance management works in practice. In addition, a literature review is included to provide a guideline for further improvements to those readers who wish to develop relevant, specific, and detailed system dynamics modeling skills and to establish the foundation for teaching system dynamics applied to performance management in organizational and inter-organizational contexts. This is particularly relevant for graduate students who have taken system dynamics courses and need to apply their own skills to business and public management.

Business. --- Project management. --- Production management. --- Dynamics. --- Ergodic theory. --- Business and Management. --- Operations Management. --- Project Management. --- Dynamical Systems and Ergodic Theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Manufacturing management --- Industrial management --- Industrial project management --- Management --- Trade --- Economics --- Commerce --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics