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| Author | : Martine Queffélec |
| Publisher | : Springer |
| Total Pages | : 252 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540480889 |
| Author | : Luís Barreira |
| Publisher | : Springer |
| Total Pages | : 223 |
| Release | : 2019-04-17 |
| Genre | : Mathematics |
| ISBN | : 3030159159 |
This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the topics include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as basic ergodic theory. As in other areas of mathematics, one can gain the first working knowledge of a topic by solving selected problems. It is rare to find large collections of problems in an advanced field of study much less to discover accompanying detailed solutions. This text fills a gap and can be used as a strong companion to an analogous dynamical systems textbook such as the authors’ own Dynamical Systems (Universitext, Springer) or another text designed for a one- or two-semester advanced undergraduate/graduate course. The book is also intended for independent study. Problems often begin with specific cases and then move on to general results, following a natural path of learning. They are also well-graded in terms of increasing the challenge to the reader. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area. Part II includes complete solutions to every problem given in Part I with each conveniently restated. Beyond basic prerequisites from linear algebra, differential and integral calculus, and complex analysis and topology, in each chapter the authors recall the notions and results (without proofs) that are necessary to treat the challenges set for that chapter, thus making the text self-contained.
| Author | : Ludwig Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662128780 |
The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
| Author | : Dhruv Khandelwal |
| Publisher | : Springer Nature |
| Total Pages | : 250 |
| Release | : 2022-02-03 |
| Genre | : Technology & Engineering |
| ISBN | : 3030903435 |
This book describes a user-friendly, evolutionary algorithms-based framework for estimating data-driven models for a wide class of dynamical systems, including linear and nonlinear ones. The methodology addresses the problem of automating the process of estimating data-driven models from a user’s perspective. By combining elementary building blocks, it learns the dynamic relations governing the system from data, giving model estimates with various trade-offs, e.g. between complexity and accuracy. The evaluation of the method on a set of academic, benchmark and real-word problems is reported in detail. Overall, the book offers a state-of-the-art review on the problem of nonlinear model estimation and automated model selection for dynamical systems, reporting on a significant scientific advance that will pave the way to increasing automation in system identification.
| Author | : Joseph H. Silverman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 482 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461208513 |
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
| Author | : Nessim Sibony |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 357 |
| Release | : 2010-07-31 |
| Genre | : Mathematics |
| ISBN | : 3642131700 |
The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
| Author | : Mark Levene |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 457 |
| Release | : 2013-03-09 |
| Genre | : Computers |
| ISBN | : 3662108747 |
The World Wide Web has become a ubiquitous global tool, used for finding infor mation, communicating ideas, carrying out distributed computation and conducting business, learning and science. The Web is highly dynamic in both the content and quantity of the information that it encompasses. In order to fully exploit its enormous potential as a global repository of information, we need to understand how its size, topology and content are evolv ing. This then allows the development of new techniques for locating and retrieving information that are better able to adapt and scale to its change and growth. The Web's users are highly diverse and can access the Web from a variety of devices and interfaces, at different places and times, and for varying purposes. We thus also need techniques for personalising the presentation and content of Web based information depending on how it is being accessed and on the specific user's requirements. As well as being accessed by human users, the Web is also accessed by appli cations. New applications in areas such as e-business, sensor networks, and mobile and ubiquitous computing need to be able to detect and react quickly to events and changes in Web-based information. Traditional approaches using query-based 'pull' of information to find out if events or changes of interest have occurred may not be able to scale to the quantity and frequency of events and changes being generated, and new 'push' -based techniques are needed.
| Author | : Luc Pronzato |
| Publisher | : CRC Press |
| Total Pages | : 240 |
| Release | : 1999-08-27 |
| Genre | : Mathematics |
| ISBN | : 9780849303364 |
Certain algorithms that are known to converge can be renormalized or "blown up" at each iteration so that their local behavior can be seen. This creates dynamical systems that we can study with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. Furthermore, we can translate the rates of convergence into less studied exponents known as Renyi entropies. This all feeds back to suggest new algorithms with faster rates of convergence. For example, in line-search, we can improve upon the Golden Section algorithm with new classes of algorithms that have their own special-and sometimes chaotic-dynamical systems. The ellipsoidal algorithms of linear and convex programming have fast, "deep cut" versions whose dynamical systems contain cyclic attractors. And ordinary steepest descent has, buried within, a beautiful fractal that controls the gateway to a special two-point attractor. Faster "relaxed" versions exhibit classical period doubling. Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization. It will prove fascinating and open doors to new areas of investigation for researchers in both fields, plus those in statistics and computer science.
| Author | : Valeri M. Mladenov |
| Publisher | : Springer |
| Total Pages | : 416 |
| Release | : 2014-06-30 |
| Genre | : Computers |
| ISBN | : 3319086723 |
This book constitutes the refereed proceedings of the 22nd International Conference on Nonlinear Dynamics of Electronic Systems, NDES 2014, held in Albena, Bulgaria, in July 2014. The 47 revised full papers presented were carefully reviewed and selected from 65 submissions. The papers are organized in topical sections on nonlinear oscillators, circuits and electronic systems; networks and nonlinear dynamics and nonlinear phenomena in biological and physiological systems.
| Author | : John Guckenheimer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 475 |
| Release | : 2013-11-21 |
| Genre | : Mathematics |
| ISBN | : 1461211409 |
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
