Dynamics In One Dimension

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Dynamics In One Dimension

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Author : Louis S. Block
language : en
Publisher: Springer
Release Date : 2006-11-14

Dynamics In One Dimension written by Louis S. Block and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The behaviour under iteration of unimodal maps of an interval, such as the logistic map, has recently attracted considerable attention. It is not so widely known that a substantial theory has by now been built up for arbitrary continuous maps of an interval. The purpose of the book is to give a clear account of this subject, with complete proofs of many strong, general properties. In a number of cases these have previously been difficult of access. The analogous theory for maps of a circle is also surveyed. Although most of the results were unknown thirty years ago, the book will be intelligible to anyone who has mastered a first course in real analysis. Thus the book will be of use not only to students and researchers, but will also provide mathematicians generally with an understanding of how simple systems can exhibit chaotic behaviour.

Topics From One Dimensional Dynamics

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Author : Karen M. Brucks
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-28

Topics From One Dimensional Dynamics written by Karen M. Brucks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-28 with Mathematics categories.

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.

Mathematical Physics In One Dimension

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Author : Elliott H. Lieb
language : en
Publisher: Academic Press
Release Date : 2013-09-17

Mathematical Physics In One Dimension written by Elliott H. Lieb and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-17 with Science categories.

Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.

Non Equilibrium Dynamics Of One Dimensional Bose Gases

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Author : Tim Langen
language : en
Publisher: Springer
Release Date : 2015-05-22

Non Equilibrium Dynamics Of One Dimensional Bose Gases written by Tim Langen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-22 with Science categories.

This work presents a series of experiments with ultracold one-dimensional Bose gases, which establish said gases as an ideal model system for exploring a wide range of non-equilibrium phenomena. With the help of newly developed tools, like full distributions functions and phase correlation functions, the book reveals the emergence of thermal-like transient states, the light-cone-like emergence of thermal correlations and the observation of generalized thermodynamic ensembles. This points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution, and lays the groundwork for a universal framework of non-equilibrium physics. The thesis investigates a central question that is highly contested in quantum physics: how and to which extent does an isolated quantum many-body system relax? This question arises in many diverse areas of physics, and many of the open problems appear at vastly different energy, time and length scales, ranging from high-energy physics and cosmology to condensed matter and quantum information. A key challenge in attempting to answer this question is the scarcity of quantum many-body systems that are both well isolated from the environment and accessible for experimental study.

Combinatorial Dynamics And Entropy In Dimension One 2nd Edition

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Author : Luis Alseda
language : en
Publisher: World Scientific Publishing Company
Release Date : 2000-10-31

Combinatorial Dynamics And Entropy In Dimension One 2nd Edition written by Luis Alseda and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-31 with Science categories.

This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.

Laws Of Chaos

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Author : Abraham Boyarsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Laws Of Chaos written by Abraham Boyarsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

A hundred years ago it became known that deterministic systems can exhibit very complex behavior. By proving that ordinary differential equations can exhibit strange behavior, Poincare undermined the founda tions of Newtonian physics and opened a window to the modern theory of nonlinear dynamics and chaos. Although in the 1930s and 1940s strange behavior was observed in many physical systems, the notion that this phenomenon was inherent in deterministic systems was never suggested. Even with the powerful results of S. Smale in the 1960s, complicated be havior of deterministic systems remained no more than a mathematical curiosity. Not until the late 1970s, with the advent of fast and cheap comput ers, was it recognized that chaotic behavior was prevalent in almost all domains of science and technology. Smale horseshoes began appearing in many scientific fields. In 1971, the phrase 'strange attractor' was coined to describe complicated long-term behavior of deterministic systems, and the term quickly became a paradigm of nonlinear dynamics. The tools needed to study chaotic phenomena are entirely different from those used to study periodic or quasi-periodic systems; these tools are analytic and measure-theoretic rather than geometric. For example, in throwing a die, we can study the limiting behavior of the system by viewing the long-term behavior of individual orbits. This would reveal incomprehensibly complex behavior. Or we can shift our perspective: Instead of viewing the long-term outcomes themselves, we can view the probabilities of these outcomes. This is the measure-theoretic approach taken in this book.

Physics In One Dimension

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Author : J. Bernasconi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Physics In One Dimension written by J. Bernasconi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

In 1966, E.H. Lieb and D.C. r1attis published a book on "Mathematical Physics in One Dimension" [Academic Press, New York and London] which is much more than just a collection of reprints and which in fact marked the beginnings of the rapidly growing interest in one-dimensional problems and materials in the 1970's. In their Foreword, Lieb and r~attis made the observation that " ... there now exists a vast literature on this subject, albeit one which is not indexed under the topic "one dimension" in standard indexing journals and which is therefore hard to research ... ". Today, the situation is even worse, and we hope that these Proceedings will be a valuable guide to some of the main current areas of one-dimensional physics. From a theoretical point of view, one-dimensional problems have always been very attractive. Many non-trivial models are soluble in one dimension, while they are only approximately understood in three dimensions. Therefore, the corresponding exact solutions serve as a useful test of approximate ma thematical methods, and certain features of the one-dimensional solution re main relevant in higher dimensions. On the other hand, many important phe nomena are strongly enhanced, and many concepts show up especially clearly in one-dimensional or quasi -one-dimensional systems. Among them are the ef fects of fluctuations, of randomness, and of nonlinearity; a number of in teresting consequences are specific to one dimension.

Nonequilibrium Statistical Mechanics In One Dimension

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Author : Vladimir Privman
language : en
Publisher: Cambridge University Press
Release Date : 1997-02-20

Nonequilibrium Statistical Mechanics In One Dimension written by Vladimir Privman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-20 with Science categories.

Self-contained and up-to-date guide to one-dimensional reactions, dynamics, diffusion and adsorption.

Dynamics In One Complex Variable

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Author : John Milnor
language : en
Publisher:
Release Date : 2014-01-15

Dynamics In One Complex Variable written by John Milnor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Newtonian Dynamics

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Author : Richard Fitzpatrick
language : en
Publisher: CRC Press
Release Date : 2021-12-24

Newtonian Dynamics written by Richard Fitzpatrick and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Science categories.

This textbook provides a comprehensive review of Newtonian dynamics at a level suitable for undergraduate physics students. It demonstrates that Newton’s three laws of motion, combined with a few simple force laws, not only can describe the motions of everyday objects observed on the surface of the Earth, but can also account for the motions of celestial objects seen in the sky. It helps bridge the problematic transition between elementary physics courses and upper-division physics courses. The book starts off at a level suitable for undergraduate (freshman) physics students and very gradually increases, until, toward the end, it approaches (but does not quite reach) a level characteristic of a graduate (senior) physics course. Each chapter of the book ends with a large number of numerical and analytical exercises and, in all appropriate cases, the final answers to the exercises are specified. The large number of exercises will allow students to accurately test their understanding of the material presented in the book, ideal for students who are self-studying or are taking classes remotely. Key Features: Provides a brief and accessible introduction to a complex topic Contains a more thorough treatment of the motions of heavenly bodies than conventional elementary mechanics texts Provides a wealth of end-of-chapter exercises to test understanding Richard Fitzpatrick is a Professor of physics at the University of Texas at Austin, USA, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of several textbooks.