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This book reviews the basic ideas of the Law of Large Numbers with
its consequences to the deterministic world and the issue of
ergodicity. Applications of Large Deviations and their outcomes to
Physics are surveyed. The book covers topics encompassing
ergodicity and its breaking and the modern applications of Large
deviations to equilibrium and non-equilibrium statistical physics,
disordered and chaotic systems, and turbulence.
Chaos: from simple models to complex systems aims to guide science
and engineering students through chaos and nonlinear dynamics from
classical examples to the most recent fields of research. The first
part, intended for undergraduate and graduate students, is a gentle
and self-contained introduction to the concepts and main tools for
the characterization of deterministic chaotic systems, with
emphasis to statistical approaches. The second part can be used as
a reference by researchers as it focuses on more advanced topics
including the characterization of chaos with tools of information
theory and applications encompassing fluid and celestial mechanics,
chemistry and biology.The book is novel in devoting attention to a
few topics often overlooked in introductory textbooks and which are
usually found only in advanced surveys such as: information and
algorithmic complexity theory applied to chaos and generalization
of Lyapunov exponents to account for spatiotemporal and
non-infinitesimal perturbations.The selection of topics, numerous
illustrations, exercises and proposals for computer experiments
make the book ideal for both introductory and advanced courses.
Chaos: from simple models to complex systems aims to guide science
and engineering students through chaos and nonlinear dynamics from
classical examples to the most recent fields of research. The first
part, intended for undergraduate and graduate students, is a gentle
and self-contained introduction to the concepts and main tools for
the characterization of deterministic chaotic systems, with
emphasis to statistical approaches. The second part can be used as
a reference by researchers as it focuses on more advanced topics
including the characterization of chaos with tools of information
theory and applications encompassing fluid and celestial mechanics,
chemistry and biology.The book is novel in devoting attention to a
few topics often overlooked in introductory textbooks and which are
usually found only in advanced surveys such as: information and
algorithmic complexity theory applied to chaos and generalization
of Lyapunov exponents to account for spatiotemporal and
non-infinitesimal perturbations.The selection of topics, numerous
illustrations, exercises and proposals for computer experiments
make the book ideal for both introductory and advanced courses.
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