Geometric Theory of Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Dynamical Systems write by J. Jr. Palis. This book was released on 2012-12-06. Geometric Theory of Dynamical Systems available in PDF, EPUB and Kindle. ... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.
Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition)
Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) write by . This book was released on 2009. Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) available in PDF, EPUB and Kindle. "This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-
Geometric Theory of Discrete Nonautonomous Dynamical Systems
Geometric Theory of Discrete Nonautonomous Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Discrete Nonautonomous Dynamical Systems write by Christian Pötzsche. This book was released on 2010-09-17. Geometric Theory of Discrete Nonautonomous Dynamical Systems available in PDF, EPUB and Kindle. The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Dynamical Systems and Geometric Mechanics
Dynamical Systems and Geometric Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamical Systems and Geometric Mechanics write by Jared Maruskin. This book was released on 2018-08-21. Dynamical Systems and Geometric Mechanics available in PDF, EPUB and Kindle. Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
Geometric Theory of Dynamical Systems
Geometric Theory of Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Dynamical Systems write by J. Jr. Palis. This book was released on 1982-08-18. Geometric Theory of Dynamical Systems available in PDF, EPUB and Kindle.
