Mathematical Tools For One Dimensional Dynamics
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Author | : Edson de Faria |
Publisher | : Cambridge University Press |
Total Pages | : 192 |
Release | : 2008-10-02 |
Genre | : Mathematics |
ISBN | : 1139474847 |
Download Mathematical Tools for One-Dimensional Dynamics Book in PDF, Epub and Kindle
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.
Author | : Edson de Faria |
Publisher | : |
Total Pages | : 100 |
Release | : 2001 |
Genre | : |
ISBN | : |
Download One Dimensional Dynamics Book in PDF, Epub and Kindle
Author | : De Faria |
Publisher | : |
Total Pages | : |
Release | : 2010-07-23 |
Genre | : |
ISBN | : 9780521170284 |
Download Mathematical Tools for One-Dimensional Dynamics ICM Edition Book in PDF, Epub and Kindle
Author | : Welington de Melo |
Publisher | : Springer Science & Business Media |
Total Pages | : 616 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642780431 |
Download One-Dimensional Dynamics Book in PDF, Epub and Kindle
One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).
Author | : Karen M. Brucks |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 2004-06-28 |
Genre | : Mathematics |
ISBN | : 9780521547666 |
Download Topics from One-Dimensional Dynamics Book in PDF, Epub and Kindle
One-dimensional dynamics owns many deep results and avenues of active mathematical research. Numerous inroads to this research exist for the advanced undergraduate or beginning graduate student. This book provides glimpses into one-dimensional dynamics with the hope that the results presented illuminate the beauty and excitement of the field. Much of this material is covered nowhere else in textbook format, some are mini new research topics in themselves, and novel connections are drawn with other research areas both inside and outside the text. The material presented here is not meant to be approached in a linear fashion. Readers are encouraged to pick and choose favourite topics. Anyone with an interest in dynamics, novice or expert alike, will find much of interest within.
Author | : Erik M. Bollt |
Publisher | : SIAM |
Total Pages | : 376 |
Release | : 2013-12-03 |
Genre | : Mathematics |
ISBN | : 1611972647 |
Download Applied and Computational Measurable Dynamics Book in PDF, Epub and Kindle
Until recently, measurable dynamics has been held as a highly theoretcal mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems. The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods.
Author | : Yoshio Kuramoto |
Publisher | : Cambridge University Press |
Total Pages | : 487 |
Release | : 2009-08-06 |
Genre | : Mathematics |
ISBN | : 0521815983 |
Download Dynamics of One-Dimensional Quantum Systems Book in PDF, Epub and Kindle
A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.
Author | : H.G Solari |
Publisher | : Routledge |
Total Pages | : 290 |
Release | : 2019-01-22 |
Genre | : Science |
ISBN | : 1351428292 |
Download Nonlinear Dynamics Book in PDF, Epub and Kindle
Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work
Author | : John Milnor |
Publisher | : Princeton University Press |
Total Pages | : 313 |
Release | : 2011-02-11 |
Genre | : Mathematics |
ISBN | : 1400835534 |
Download Dynamics in One Complex Variable Book in PDF, Epub and Kindle
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.
Author | : Maria José Pacifico |
Publisher | : Springer Nature |
Total Pages | : 333 |
Release | : 2019-12-14 |
Genre | : Mathematics |
ISBN | : 3030168336 |
Download New Trends in One-Dimensional Dynamics Book in PDF, Epub and Kindle
This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016. Highlighting the latest results in one-dimensional dynamics and its applications, the contributions gathered here also celebrate the highly successful meeting, which brought together experts in the field, including many of Welington de Melo’s co-authors and former doctoral students. Sadly, Welington de Melo passed away shortly after the conference, so that the present volume became more a tribute to him. His role in the development of mathematics was undoubtedly an important one, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are required reading for all newcomers to the field.