Dynamical Systems Theory

e-books in Dynamical Systems Theory category

Random Differential Equations in Scientific Computing
by Tobias Neckel, Florian Rupp - De Gruyter Open , 2013
This book is a self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering both dynamical systems and scientific computing.
(4784 views)

Fractal Analysis
by Sid-Ali Ouadfeul (ed.) - InTech , 2019
The aim of this book is to show some applications of fractal analysis in the sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets...
(5659 views)

Chaos Theory
by Kais A. Mohamedamen Al Naimee (ed.) - InTech , 2018
With a good background in nonlinear dynamics, chaos theory, and applications, the authors give a treatment of the basic principles of nonlinear dynamics in different fields. In addition, they show overlap with the traditional field of control theory.
(6859 views)

Data Assimilation: A Mathematical Introduction
by K.J.H. Law, A.M. Stuart, K.C. Zygalakis - arXiv.org , 2015
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation. Authors develop a framework in which a Bayesian formulation of the problem provides the bedrock for the derivation and analysis of algorithms.
(6127 views)

Dynamical Systems: Analytical and Computational Techniques
by Mahmut Reyhanoglu - InTech , 2017
There has been a considerable progress made during the recent past on mathematical techniques for studying dynamical systems. This progress is due to our increasing ability to mathematically model physical processes and to analyze and solve them.
(7024 views)

Extremes and Recurrence in Dynamical Systems
by Valerio Lucarini, et al. - arXiv , 2016
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. It provides an overview of the area, underlining its relevance for mathematics, natural sciences, engineering, and social sciences.
(5779 views)

Dynamical Systems
by Jose A. Tenreiro Machado (ed.) - MDPI AG , 2014
Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematics. This volume intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community.
(6858 views)

Around the Boundary of Complex Dynamics
by Roland K. W. Roeder - arXiv , 2015
We introduce the exciting field of complex dynamics at an undergraduate level while reviewing, reinforcing, and extending the ideas learned in an typical first course on complex analysis. Julia sets and the famous Mandelbrot set will be introduced...
(6627 views)

Hyperbolic Manifolds, Discrete Groups and Ergodic Theory
by Curtis T. McMullen - Harvard University , 2011
Contents: Ergodic theory; Dynamics on hyperbolic surfaces; Orbit counting, equidistribution and arithmetic; Spectral theory; Mixing of unitary representations of SLnR; Amenability; The Laplacian; All unitary representations of PSL2(R); etc.
(8623 views)

Variational Modelling: Energies, gradient flows, and large deviations
by Mark A. Peletier - arXiv , 2014
The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the methodology itself in great detail, and explain why this is a rational modelling route.
(9418 views)

Complex Dynamics and Renormalization
by Curtis T. McMullen - Princeton University Press , 1994
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics.
(8859 views)

Perturbation Theory of Dynamical Systems
by Nils Berglund - arXiv , 2001
These are lecture notes for undergraduate Mathematics and Physics students. They cover a few selected topics from perturbation theory at an introductory level: Bifurcations and Unfolding; Regular Perturbation Theory; Singular Perturbation Theory.
(6954 views)

Stability Analysis via Matrix Functions Method
by A. A. Martynyuk - Bookboon , 2013
The monograph presents a generalization of the well-known Lyapunov function method and related concepts to the matrix function case within the framework of systematic stability analysis of dynamical systems (differential equations).
(9524 views)

Ergodic Optimization, Zero Temperature Limits and the Max-plus Algebra
by A. T. Baraviera, R. Leplaideur, A. O. Lopes - arXiv , 2013
We review some basic notions in ergodic theory and thermodynamic formalism, as well as introductory results in the context of max-plus algebra, in order to exhibit some properties of equilibrium measures when temperature goes to zero.
(7809 views)

Discrete Dynamical Systems
by Arild Wikan - Bookboon , 2013
This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential to understand the behavior of nonlinear discrete dynamical systems. The theory is illuminated by examples and exercises.
(8491 views)

Lectures on Topics In One-Parameter Bifurcation Problems
by P. Rabier - Tata Institute of Fundamental Research , 1985
This set of lectures gives a synthetic exposition for the study of one-parameter bifurcation problems. By this, we mean the analysis of the structure of their set of solutions through the same type of general arguments in various situations.
(9514 views)

Singularities of Transition Processes in Dynamical Systems
by Alexander N. Gorban - American Mathematical Society , 2004
This monograph presents a systematic analysis of the singularities in the transition processes for dynamical systems. We study general dynamical systems, with dependence on a parameter, and construct relaxation times that depend on three variables.
(10041 views)

Substitutions in Dynamics, Arithmetics, and Combinatorics
by Pierre Arnoux, et al. - Springer , 2002
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules.
(10865 views)

Computable Integrability
by Alexey Shabat, Elena Kartashova - arXiv , 2011
A preliminary version of the textbook on integrable systems. Contents: General notions and ideas; Riccati equation; Factorization of linear operators; Commutativity of linear operators; Integrability of non-linear PDEs; Burgers-type equations.
(10186 views)

Dynamical Systems
by Shlomo Sternberg - OER Commons , 2000
This book addresses the following topics: Iterations and fixed points; bifurcations; conjugacy; space and time averages; the contraction fixed point theorem; Hutchinson's theorem and fractal images; hyperbolicity; and symbolic dynamics.
(11129 views)

Valuations and Hyperbolicity in Dynamics
by Thomas Ward - University of East Anglia , 2001
These notes describe several situations in dynamics where the notion of valuations on rings provides a simple language in which to describe and exploit hyperbolicity. This approach goes a little beyond simply providing a convenient language.
(9277 views)

Entropy of Compact Group Automorphisms
by Thomas Ward - University of East Anglia , 2001
These notes cover a very short introduction to measure-theoretic and topological entropy, and are aimed at understanding part of Yuzvinskii's formula for the entropy of compact group automorphisms. Based on a course at the Ohio State University.
(9296 views)

Elementary Symbolic Dynamics and Chaos in Dissipative Systems
by Bai-Lin Hao - World Scientific , 1989
This is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and characteristics of the attractors, written from the view-point of practical applications.
(10250 views)

Introduction to Dynamical Systems: A Hands-on Approach with Maxima
by Jaime E. Villate , 2006
In this book we explore some topics on dynamical systems, using an active teaching approach, supported by computing tools. The subject of this book on dynamical systems is at the borderline of physics, mathematics and computing.
(11278 views)

Monotone Dynamical Systems
by M.W. Hirsch, Hal Smith , 2004
From the table of contents: Introduction; Strongly Order-Preserving Semiflows; Generic Convergence and Stability; Ordinary Differential Equations; Delay Differential Equations; Monotone Maps; Semilinear Parabolic Equations.
(11816 views)

Mathematical Principles of Dynamic Systems and the Foundations of Quantum Physics
by Eric Tesse - arXiv , 2012
This article will take up the question of what underlies the quantum formalism, whether it can be derived from simpler mathematical structures, and if so, what physical properties a system must possess in order for the formalism to hold.
(11694 views)

Local Theory of Holomorphic Foliations and Vector Fields
by Julio C. Rebelo, Helena Reis - arXiv , 2011
Informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differ slightly from the classical arguments.
(10036 views)

Geometrical Theory of Dynamical Systems
by Nils Berglund - arXiv , 2001
This text is a slightly edited version of lecture notes for a course to undergraduate Mathematics and Physics students. Contents: Examples of Dynamical Systems; Stationary and Periodic Solutions; Local Bifurcations; Introduction to Chaotic Dynamics.
(10888 views)

A Short Introduction to Classical and Quantum Integrable Systems
by O. Babelon , 2007
An introduction to integrable systems. From the table of contents: Integrable dynamical systems; Solution by analytical methods; Infinite dimensional systems; The Jaynes-Cummings-Gaudin model; The Heisenberg spin chain; Nested Bethe Ansatz.
(12609 views)

An Introduction to Quantum Chaos
by Mason A. Porter - arXiv , 2001
Nonlinear dynamics (''chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The author gives a brief review of the origin and fundamentals of both quantum mechanics and nonlinear dynamics.
(13061 views)

Complex and Adaptive Dynamical Systems: A Primer
by Claudius Gros - arXiv , 2008
This textbook covers a wide range of concepts, notions and phenomena of a truly interdisciplinary subject. Complex system theory deals with dynamical systems containing a very large number of variables, showing a plethora of emergent features.
(14965 views)

Optimization and Dynamical Systems
by U. Helmke, J. B. Moore - Springer , 1996
Aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control systems, signal processing, and linear algebra. The problems solved are those of linear algebra and linear systems theory.
(14558 views)

Dynamics, Ergodic Theory, and Geometry
by Boris Hasselblatt - Cambridge University Press , 2007
This book contains articles in several areas of dynamical systems that have recently experienced substantial progress. Some of the major surveys focus on symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; etc.
(16196 views)

Encyclopedia of Dynamical Systems
by D. Anosov, at al. - Scholarpedia , 2009
The encyclopedia covers differential equations, numerical analysis, bifurcations, topological dynamics, ergodic theory, hyperbolic dynamics, oscillators, pattern formation, chaos, statistical mechanics, control theory, and applications.
(13364 views)

The Chaos Hypertextbook
by Glenn Elert , 2007
This book is written for anyone with an interest in chaos, fractals, non-linear dynamics, or mathematics in general. It's a moderately heavy piece of work, requiring a bit of mathematical knowledge, but it is definitely not aimed at mathematicians.
(14055 views)

The Hopf Bifurcation and Its Applications
by J. E. Marsden, M. McCracken - Springer , 1976
The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, including stability calculations.
(14264 views)

Ordinary Differential Equations and Dynamical Systems
by Gerald Teschl - Universitaet Wien , 2009
This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem.
(16667 views)

Dynamical Systems and Chaos
by Evans M. Harrell II , 2000
Class notes for an introductory course on dynamical systems and chaos for mathematicians, physicists, and engineers. The text concentrates on models rather than proofs in order to bring out the concepts of dynamics and chaos.
(15298 views)

Introduction to the Theory of Infinite-Dimensional Dissipative Systems
by Constantin I. Chueshov - ACTA , 2002
An introduction to infinite-dimensional dissipative dynamical systems. The book outlines a variety of tools applied in the study of nonlinear dynamical distributed systems. The results have applications to many areas of physics and engineering.
(11722 views)

Chaos: Classical and Quantum
by Predrag Cvitanovic - ChaosBook.org , 2008
This is a graduate textbook on classical and quantum chaos, applicable to problems of physics, chemistry and other sciences. It represents an attempt to formulate the subject as one of the cornerstones of the graduate physics curriculum of future.
(16072 views)

Invitation to Dynamical Systems
by Edward R. Scheinerman - Prentice Hall College Div , 2000
Author invites readers from a wide range of backgrounds to explore the beauty and excitement of dynamical systems. Written for readers who want to continue exploring mathematics beyond linear algebra, but are not ready for highly abstract material.
(17851 views)

Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry
by Florentin Smarandache - Amer Research Pr , 2000
A collection of definitions, questions, and theorems such as Smarandache type conjectures, problems, numerical bases, T-numbers, progressions, series, functions, Non-Euclidean geometries, paradoxes, linguistic tautologies, and more.
(17966 views)