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Dynamical Systems Theory

e-books in Dynamical Systems Theory category

Book cover: Dynamical Systems: Analytical and Computational TechniquesDynamical Systems: Analytical and Computational Techniques
by - InTech ,
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.
(897 views)
Book cover: Extremes and Recurrence in Dynamical SystemsExtremes and Recurrence in Dynamical Systems
by - arXiv ,
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.
(646 views)

Book cover: Dynamical SystemsDynamical Systems
by - MDPI AG ,
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.
(1500 views)
Book cover: Around the Boundary of Complex DynamicsAround the Boundary of Complex Dynamics
by - arXiv ,
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...
(1733 views)
Book cover: Hyperbolic Manifolds, Discrete Groups and Ergodic TheoryHyperbolic Manifolds, Discrete Groups and Ergodic Theory
by - Harvard University ,
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.
(2675 views)
Book cover: Variational Modelling: Energies, gradient flows, and large deviationsVariational Modelling: Energies, gradient flows, and large deviations
by - arXiv ,
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.
(3997 views)
Book cover: Complex Dynamics and RenormalizationComplex Dynamics and Renormalization
by - Princeton University Press ,
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.
(3947 views)
Book cover: Perturbation Theory of Dynamical SystemsPerturbation Theory of Dynamical Systems
by - arXiv ,
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.
(2081 views)
Book cover: Stability Analysis via Matrix Functions MethodStability Analysis via Matrix Functions Method
by - Bookboon ,
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).
(4030 views)
Book cover: Ergodic Optimization, Zero Temperature Limits and the Max-plus AlgebraErgodic Optimization, Zero Temperature Limits and the Max-plus Algebra
by - arXiv ,
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.
(2304 views)
Book cover: Discrete Dynamical SystemsDiscrete Dynamical Systems
by - Bookboon ,
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.
(2935 views)
Book cover: Lectures on Topics In One-Parameter Bifurcation ProblemsLectures on Topics In One-Parameter Bifurcation Problems
by - Tata Institute of Fundamental Research ,
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.
(4298 views)
Book cover: Singularities of Transition Processes in Dynamical SystemsSingularities of Transition Processes in Dynamical Systems
by - American Mathematical Society ,
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.
(4500 views)
Book cover: Substitutions in Dynamics, Arithmetics, and CombinatoricsSubstitutions in Dynamics, Arithmetics, and Combinatorics
by - Springer ,
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.
(5567 views)
Book cover: Computable IntegrabilityComputable Integrability
by - arXiv ,
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.
(4086 views)
Book cover: Dynamical SystemsDynamical Systems
by - OER Commons ,
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.
(5020 views)
Book cover: Valuations and Hyperbolicity in DynamicsValuations and Hyperbolicity in Dynamics
by - University of East Anglia ,
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.
(3993 views)
Book cover: Entropy of Compact Group AutomorphismsEntropy of Compact Group Automorphisms
by - University of East Anglia ,
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.
(3911 views)
Book cover: Elementary Symbolic Dynamics and Chaos in Dissipative SystemsElementary Symbolic Dynamics and Chaos in Dissipative Systems
by - World Scientific ,
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.
(5267 views)
Book cover: An Introduction to Dynamical Systems and ChaosAn Introduction to Dynamical Systems and Chaos
by - LDEO ,
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.
(5375 views)
Book cover: Introduction to Dynamical Systems: A Hands-on Approach with MaximaIntroduction to Dynamical Systems: A Hands-on Approach with Maxima
by ,
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.
(5506 views)
Book cover: Monotone Dynamical SystemsMonotone Dynamical Systems
by ,
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.
(5408 views)
Book cover: Local Theory of Holomorphic Foliations and Vector FieldsLocal Theory of Holomorphic Foliations and Vector Fields
by - arXiv ,
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.
(4397 views)
Book cover: Geometrical Theory of Dynamical SystemsGeometrical Theory of Dynamical Systems
by - arXiv ,
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.
(5600 views)
Book cover: A Short Introduction to Classical and Quantum Integrable SystemsA Short Introduction to Classical and Quantum Integrable Systems
by ,
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.
(6494 views)
Book cover: An Introduction to Quantum ChaosAn Introduction to Quantum Chaos
by - arXiv ,
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.
(6343 views)
Book cover: Complex and Adaptive Dynamical Systems: A PrimerComplex and Adaptive Dynamical Systems: A Primer
by - arXiv ,
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.
(8778 views)
Book cover: Optimization and Dynamical SystemsOptimization and Dynamical Systems
by - Springer ,
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.
(8022 views)
Book cover: Dynamics, Ergodic Theory, and GeometryDynamics, Ergodic Theory, and Geometry
by - Cambridge University Press ,
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.
(10068 views)
Book cover: Encyclopedia of Dynamical SystemsEncyclopedia of Dynamical Systems
by - Scholarpedia ,
The encyclopedia covers differential equations, numerical analysis, bifurcations, topological dynamics, ergodic theory, hyperbolic dynamics, oscillators, pattern formation, chaos, statistical mechanics, control theory, and applications.
(7753 views)
Book cover: The Chaos HypertextbookThe Chaos Hypertextbook
by ,
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.
(8480 views)
Book cover: The Hopf Bifurcation and Its ApplicationsThe Hopf Bifurcation and Its Applications
by - Springer ,
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.
(7995 views)
Book cover: Ordinary Differential Equations and Dynamical SystemsOrdinary Differential Equations and Dynamical Systems
by - Universitaet Wien ,
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.
(10225 views)
Book cover: Dynamical Systems and ChaosDynamical Systems and Chaos
by ,
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.
(9510 views)
Book cover: Introduction to the Theory of Infinite-Dimensional Dissipative SystemsIntroduction to the Theory of Infinite-Dimensional Dissipative Systems
by - ACTA ,
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.
(6186 views)
Book cover: Chaos: Classical and QuantumChaos: Classical and Quantum
by - ChaosBook.org ,
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.
(10222 views)
Book cover: Invitation to Dynamical SystemsInvitation to Dynamical Systems
by - Prentice Hall College Div ,
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.
(10337 views)