## e-books in Dynamical Systems Theory category

**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.

(

**515**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.

(

**1097**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.

(

**789**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.

(

**1724**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...

(

**1937**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.

(

**2827**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.

(

**4167**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.

(

**4117**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.

(

**2234**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).

(

**4196**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.

(

**2490**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.

(

**3145**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.

(

**4454**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.

(

**4737**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.

(

**5750**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.

(

**4358**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.

(

**5294**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.

(

**4208**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.

(

**4057**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.

(

**5435**views)

**An Introduction to Dynamical Systems and Chaos**

by

**Marc Spiegelman**-

**LDEO**,

**1997**

This tutorial will develop the basics ingredients necessary for modeling simple non-linear dynamical systems. The goal is to demonstrate you that you can develop significant insight into the behavior of non-linear systems with just a little math.

(

**5621**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.

(

**5681**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.

(

**5636**views)

**Mathematical Principals of Dynamic Systems and the Foundations of Quantum Physics**

by

**Eric Tesse**-

**arXiv**,

**2011**

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.

(

**5704**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.

(

**4558**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.

(

**5819**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.

(

**6717**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.

(

**6737**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.

(

**9064**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.

(

**8334**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.

(

**10235**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.

(

**7930**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.

(

**8647**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.

(

**8219**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.

(

**10464**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.

(

**9682**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.

(

**6376**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.

(

**10414**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.

(

**10597**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.

(

**11864**views)