Number Theory and Dynamical Systems
Number Theory and Dynamical Systems

Author: M. M. Dodson

Publisher: Cambridge University Press

Published: 1989-11-09

Total Pages: 185

ISBN-13: 0521369193

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This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.

Mathematics of Complexity and Dynamical Systems
Mathematics of Complexity and Dynamical Systems

Author: Robert A. Meyers

Publisher: Springer Science & Business Media

Published: 2011-10-05

Total Pages: 1885

ISBN-13: 1461418054

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Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Dynamical Systems and Chaos
Dynamical Systems and Chaos

Author: Henk Broer

Publisher: Springer Science & Business Media

Published: 2010-10-20

Total Pages: 313

ISBN-13: 1441968709

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Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.

From Number Theory to Physics
From Number Theory to Physics

Author: Michel Waldschmidt

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 702

ISBN-13: 3662028387

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The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.

Handbook of Dynamical Systems
Handbook of Dynamical Systems

Author: H. Broer

Publisher: Elsevier

Published: 2010-11-10

Total Pages: 556

ISBN-13: 0080932266

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In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. - Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems - Highlights developments that are the foundation for future research in this field - Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Dynamical Systems and Small Divisors
Dynamical Systems and Small Divisors

Author: Hakan Eliasson

Publisher: Springer

Published: 2004-10-11

Total Pages: 207

ISBN-13: 3540479287

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Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.

The Method of Intrinsic Scaling
The Method of Intrinsic Scaling

Author: José Miguel Urbano

Publisher: Springer Science & Business Media

Published: 2008-05-20

Total Pages: 158

ISBN-13: 354075931X

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This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs.In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions.

Algebraic Groups and Lie Groups with Few Factors
Algebraic Groups and Lie Groups with Few Factors

Author: Alfonso Di Bartolo

Publisher: Springer Science & Business Media

Published: 2008-04-17

Total Pages: 223

ISBN-13: 3540785833

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This volume treats algebraic groups from a group theoretical point of view and compares the results with the analogous issues in the theory of Lie groups. It examines a classification of algebraic groups and Lie groups having only few subgroups.

The Tyranny of Uncertainty
The Tyranny of Uncertainty

Author: Nabil Abu el Ata

Publisher: Springer

Published: 2016-05-17

Total Pages: 375

ISBN-13: 3662491044

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The authors offer a revolutionary solution to risk management. It’s the unknown risks that keep leaders awake at night—wondering how to prepare for and steer their organization clear from that which they cannot predict. Businesses, governments and regulatory bodies dedicate endless amounts of time and resources to the task of risk management, but every leader knows that the biggest threats will come from some new chain of events or unexpected surprises—none of which will be predicted using conventional wisdom or current risk management technologies and so management will be caught completely off guard when the next crisis hits. By adopting a scientific approach to risk management, we can escape the limited and historical view of experience and statistical based risk management models to expose dynamic complexity risks and prepare for new and never experienced events.

Working with Dynamical Systems
Working with Dynamical Systems

Author: Len Pismen

Publisher: CRC Press

Published: 2020-12-15

Total Pages: 250

ISBN-13: 0429950152

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This book provides working tools for the study and design of nonlinear dynamical systems applicable in physics and engineering. It offers a broad-based introduction to this challenging area of study, taking an applications-oriented approach that emphasizes qualitative analysis and approximations rather than formal mathematics or simulation. The author, an internationally recognized authority in the field, makes extensive use of examples and includes executable Mathematica notebooks that may be used to generate new examples as hands-on exercises. The coverage includes discussion of mechanical models, chemical and ecological interactions, nonlinear oscillations and chaos, forcing and synchronization, spatial patterns and waves. Key Features: Written for a broad audience, avoiding dependence on mathematical formulations in favor of qualitative, constructive treatment Extensive use of physical and engineering applications Incorporates Mathematica notebooks for simulations and hands-on self-study Provides a gentle but rigorous introduction to real-world nonlinear problems Features a final chapter dedicated to applications of dynamical systems to spatial patterns The book is aimed at student and researchers in applied mathematics and mathematical modelling of physical and engineering problems. It teaches to see common features in systems of different origins, and to apply common methods of study without losing sight of complications and uncertainties related to their physical origin.