Dynamical Systems on 2- and 3-Manifolds - 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 on 2- and 3-Manifolds write by Viacheslav Z. Grines. This book was released on 2016-11-11. Dynamical Systems on 2- and 3-Manifolds available in PDF, EPUB and Kindle. This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.“br> The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.
Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds
Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds - 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 Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds write by A.K. Prykarpatsky. This book was released on 2012-10-10. Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds available in PDF, EPUB and Kindle. In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Topology and Geometry of Manifolds
Topology and Geometry of Manifolds - 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 Topology and Geometry of Manifolds write by Gordana Matic. This book was released on 2003. Topology and Geometry of Manifolds available in PDF, EPUB and Kindle. Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.
Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142
Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 - 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 Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 write by Curtis T. McMullen. This book was released on 2014-09-08. Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 available in PDF, EPUB and Kindle. Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Foliations and the Geometry of 3-Manifolds
Foliations and the Geometry of 3-Manifolds - 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 Foliations and the Geometry of 3-Manifolds write by Danny Calegari. This book was released on 2007-05-17. Foliations and the Geometry of 3-Manifolds available in PDF, EPUB and Kindle. This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
