Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach PDF full book. Access full book title Randomness and Recurrence in Dynamical Systems: A Real Analysis Approach by Rodney Nillsen. Download full books in PDF and EPUB format.
Author: Rodney Nillsen
Publisher: American Mathematical Soc.
ISBN: 0883850435
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
Book Description
Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Lévy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.
Author: Rodney Nillsen
Publisher: American Mathematical Soc.
ISBN: 0883850435
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
Book Description
Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Lévy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.
Author: Valerio Lucarini
Publisher: John Wiley & Sons
ISBN: 1118632192
Category : Mathematics
Languages : en
Pages : 325
Get Book Here
Book Description
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Author: Rabi Bhattacharya
Publisher: Cambridge University Press
ISBN: 1139461621
Category : Mathematics
Languages : en
Pages : 5
Get Book Here
Book Description
This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.
Author: Fritz Colonius
Publisher: American Mathematical Society
ISBN: 0821883194
Category : Mathematics
Languages : en
Pages : 302
Get Book Here
Book Description
This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝd and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students.
Author: Rodney Nillsen
Publisher: MAA Press
ISBN: 9781614440000
Category : Differentiable dynamical systems
Languages : en
Pages : 376
Get Book Here
Book Description
Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background--
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 1139460889
Category : Mathematics
Languages : en
Pages : 203
Get Book Here
Book Description
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author: Jane Hawkins
Publisher: American Mathematical Soc.
ISBN: 1470448319
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
Book Description
This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13–15, 2018, at Agnes Scott College, Decatur, Georgia. The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages. The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.
Author: Mark I. Freidlin
Publisher: Springer Science & Business Media
ISBN: 3642258476
Category : Mathematics
Languages : en
Pages : 483
Get Book Here
Book Description
Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been “rediscovered” in applied papers. In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained. Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important.
Author: M. I. Freidlin
Publisher: Springer Science & Business Media
ISBN: 1468401769
Category : Mathematics
Languages : en
Pages : 334
Get Book Here
Book Description
Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.
Author: Russell Johnson
Publisher: American Mathematical Soc.
ISBN: 0821808656
Category : Computers
Languages : en
Pages : 63
Get Book Here
Book Description
This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.
