A First Course In Discrete Dynamical Systems
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A First Course In Discrete Dynamical Systems
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Author : Richard A. Holmgren
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A First Course In Discrete Dynamical Systems written by Richard A. Holmgren 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.
An increasing number of colleges and universities are offering undergradu ate courses in discrete dynamical systems. This growth is due in part to the proliferation of inexpensive and powerful computers, which have provided access to the interesting and complex phenomena that are at the heart of dynamics. A second reason for introducing dynamics into the undergradu ate curriculum is that it serves as a bridge from concrete, often algorithmic calculus courses, to the more abstract concepts of analysis and topology. Discrete dynamical systems are essentially iterated functions, and if there is one thing computers do well, it is iteration. It is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Every effort has been made to exploit this opportunity to illustrate the beauty and power of mathematics in an interesting and engaging way. This work is first and foremost a mathematics book. Individuals who read it and do the exercises will gain not only an understanding of dynamical systems, but an increased understanding of the related areas in analysis as well.
A First Course In Discrete Dynamical Systems
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Author : Richard A Holmgren
language : en
Publisher:
Release Date : 1996-08-01
A First Course In Discrete Dynamical Systems written by Richard A Holmgren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-01 with categories.
An Introduction To Dynamical Systems
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Author : Rex Clark Robinson
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
An Introduction To Dynamical Systems written by Rex Clark Robinson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.
A First Course In Dynamics
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Author : Boris Hasselblatt
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-23
A First Course In Dynamics written by Boris Hasselblatt 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 2003-06-23 with Mathematics categories.
The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
A First Course In Fuzzy Logic Fuzzy Dynamical Systems And Biomathematics
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Author : Laécio Carvalho de Barros
language : en
Publisher: Springer
Release Date : 2016-09-13
A First Course In Fuzzy Logic Fuzzy Dynamical Systems And Biomathematics written by Laécio Carvalho de Barros and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-13 with Technology & Engineering categories.
This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics.
Dynamical Systems
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Author : Luis Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-02
Dynamical Systems written by Luis Barreira 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 2012-12-02 with Mathematics categories.
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
Advanced Topics In The Arithmetic Of Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Advanced Topics In The Arithmetic Of Elliptic Curves written by Joseph H. Silverman 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 2013-12-01 with Mathematics categories.
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.
Applications Of Advanced Optimization Techniques In Industrial Engineering
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Author : Abhinav Goel
language : en
Publisher: CRC Press
Release Date : 2022-03-09
Applications Of Advanced Optimization Techniques In Industrial Engineering written by Abhinav Goel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-09 with Mathematics categories.
This book provides different approaches used to analyze, draw attention, and provide an understanding of the advancements in the optimization field across the globe. It brings all of the latest methodologies, tools, and techniques related to optimization and industrial engineering into a single volume to build insights towards the latest advancements in various domains. Applications of Advanced Optimization Techniques in Industrial Engineering includes the basic concept of optimization, techniques, and applications related to industrial engineering. Concepts are introduced in a sequential way along with explanations, illustrations, and solved examples. The book goes on to explore applications of operations research and covers empirical properties of a variety of engineering disciplines. It presents network scheduling, production planning, industrial and manufacturing system issues, and their implications in the real world. The book caters to academicians, researchers, professionals in inventory analytics, business analytics, investment managers, finance firms, storage-related managers, and engineers working in engineering industries and data management fields.
Economic Dynamics
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Author : Ronald Shone
language : en
Publisher: Cambridge University Press
Release Date : 2002-11-28
Economic Dynamics written by Ronald Shone 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 2002-11-28 with Business & Economics categories.
This is the substantially revised and restructured second edition of Ron Shone's successful advanced textbook Economic Dynamics. The book provides detailed coverage of dynamics and phase diagrams, including: quantitative and qualitative dynamic systems, continuous and discrete dynamics, linear and non-linear systems and single equation and systems of equations. It illustrates dynamic systems using Mathematica, Maple V and spreadsheets. It provides a thorough introduction to phase diagrams and their economic application and explains the nature of saddle path solutions. The second edition contains a new chapter on oligopoly and an extended treatment of stability of discrete dynamic systems and the solving of first-order difference equations. Detailed routines on the use of Mathematica and Maple are now contained in the body of the text, which now includes advice on the use of Excel and additional examples and exercises throughout. Supporting website contains solutions manual and learning tools.