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Lectures on Lyapunov Exponents

2014-07-24 Mathematics
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Release : 2014-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 694/5 ( reviews)

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Book Synopsis Lectures on Lyapunov Exponents by : Marcelo Viana

Download or read book Lectures on Lyapunov Exponents written by Marcelo Viana. This book was released on 2014-07-24. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.

Local Lyapunov Exponents

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 632/5 ( reviews)

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Book Synopsis Local Lyapunov Exponents by : Wolfgang Siegert

Download or read book Local Lyapunov Exponents written by Wolfgang Siegert. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.

Lyapunov Exponents

2017-12-30 Mathematics
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Release : 2017-12-30
Genre : Mathematics
Kind : eBook
Book Rating : 616/5 ( reviews)

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Book Synopsis Lyapunov Exponents by : Luís Barreira

Download or read book Lyapunov Exponents written by Luís Barreira. This book was released on 2017-12-30. Available in PDF, EPUB and Kindle. Book excerpt: 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

2016-02-11 Science
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Release : 2016-02-11
Genre : Science
Kind : eBook
Book Rating : 708/5 ( reviews)

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Book Synopsis Lyapunov Exponents by : Arkady Pikovsky

Download or read book Lyapunov Exponents written by Arkady Pikovsky. This book was released on 2016-02-11. Available in PDF, EPUB and Kindle. Book excerpt: Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.

Lyapunov Exponents

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 957/5 ( reviews)

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Book Synopsis Lyapunov Exponents by : Ludwig Arnold

Download or read book Lyapunov Exponents written by Ludwig Arnold. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt:

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