Dynamical Systems On 2 And 3 Manifolds
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Dynamical Systems On 2 And 3 Manifolds
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Author : Viacheslav Z. Grines
language : en
Publisher: Springer
Release Date : 2016-11-11
Dynamical Systems On 2 And 3 Manifolds written by Viacheslav Z. Grines and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-11 with Mathematics categories.
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.
Foliations And The Geometry Of 3 Manifolds
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Author : Danny Calegari
language : en
Publisher: OUP Oxford
Release Date : 2007-05-17
Foliations And The Geometry Of 3 Manifolds written by Danny Calegari and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-17 with Mathematics categories.
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 in 1-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.
Linear Time Varying Approximations To Nonlinear Dynamical Systems
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Author : Maria Tomas-Rodriguez
language : en
Publisher: Springer
Release Date : 2010-01-12
Linear Time Varying Approximations To Nonlinear Dynamical Systems written by Maria Tomas-Rodriguez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-12 with Mathematics categories.
Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.
Recent Improvements In The Theory Of Chaotic Attractors
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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2025-02-19
Recent Improvements In The Theory Of Chaotic Attractors written by René Lozi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-19 with Mathematics categories.
This book presents some exceptional developments in chaotic attractor theory encompassing several new directions of research such as three-dimensional axiom A-diffeomorphisms, Shilnikov attractors, dendrites and finite graphs. The theory of chaotic attractors has experienced exceptional development over the last fifty years since the revelation of chaos in mathematics (invented by James Yorke) and symbolized by the “butterfly effect”. Relevant new results have been collected in this book, including: Some remarks on minimal sets on dendrites and finite graphs and the study of recurrence and nonwandering sets of local dendrite maps. Ramified continua as global attractors of C1- smooth self-maps of a cylinder close to skew products Chaotic behaviour of countable products of homeomorphism groups and dynamics of three-dimensional axiom A-diffeomorphisms with two-dimensional attractors and repellers. The search for invariant sets of the generalized tent map and quasi-hyperbolic regime in a certain family of 2-D piecewise linear map. Shilnikov attractors of three-dimensional flows and maps, right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis and diffeomorphisms with infinitely many Smale horseshoes. The theory of chaotic attractor is also used as a core for evolutionary algorithms and metaheuristic optimizers in this volume. This book will be of great value to students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications. The chapters in this book were originally published in Journal of Difference Equations and Applications.
Dynamical Systems And Applications
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Author : Ravi P Agarwal
language : en
Publisher: World Scientific
Release Date : 1995-11-07
Dynamical Systems And Applications written by Ravi P Agarwal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-07 with Mathematics categories.
World Scientific series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. For the past twenty five years, there has been an explosion of interest in the study of nonlinear dynamical systems. Mathematical techniques developed during this period have been applied to important nonlinear problems ranging from physics and chemistry to ecology and economics. All these developments have made dynamical systems theory an important and attractive branch of mathematics to scientists in many disciplines. This rich mathematical subject has been partially represented in this collection of 45 papers by some of the leading researchers in the area. This volume contains 45 state-of-art articles on the mathematical theory of dynamical systems by leading researchers. It is hoped that this collection will lead new direction in this field.Contributors: B Abraham-Shrauner, V Afraimovich, N U Ahmed, B Aulbach, E J Avila-Vales, F Battelli, J M Blazquez, L Block, T A Burton, R S Cantrell, C Y Chan, P Collet, R Cushman, M Denker, F N Diacu, Y H Ding, N S A El-Sharif, J E Fornaess, M Frankel, R Galeeva, A Galves, V Gershkovich, M Girardi, L Gotusso, J Graczyk, Y Hino, I Hoveijn, V Hutson, P B Kahn, J Kato, J Keesling, S Keras, V Kolmanovskii, N V Minh, V Mioc, K Mischaikow, M Misiurewicz, J W Mooney, M E Muldoon, S Murakami, M Muraskin, A D Myshkis, F Neuman, J C Newby, Y Nishiura, Z Nitecki, M Ohta, G Osipenko, N Ozalp, M Pollicott, Min Qu, Donal O-Regan, E Romanenko, V Roytburd, L Shaikhet, J Shidawara, N Sibony, W-H Steeb, C Stoica, G Swiatek, T Takaishi, N D Thai Son, R Triggiani, A E Tuma, E H Twizell, M Urbanski; T D Van, A Vanderbauwhede, A Veneziani, G Vickers, X Xiang, T Young, Y Zarmi.
Renormalization And 3 Manifolds Which Fiber Over The Circle
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Author : Curtis T. McMullen
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08
Renormalization And 3 Manifolds Which Fiber Over The Circle written by Curtis T. McMullen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.
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.
In The Tradition Of Thurston Ii
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2022-08-02
In The Tradition Of Thurston Ii written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Mathematics categories.
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Foliations Geometry And Dynamics Proceedings Of The Euroworkshop
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Author : Lawrence Conlon
language : en
Publisher: World Scientific
Release Date : 2002-02-01
Foliations Geometry And Dynamics Proceedings Of The Euroworkshop written by Lawrence Conlon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-01 with categories.
This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets.
Topology 90
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-10-13
Topology 90 written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
No detailed description available for "Topology '90".
Differential Topology Foliations And Group Actions
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Author : Paul A. Schweitzer
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Differential Topology Foliations And Group Actions written by Paul A. Schweitzer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions---finite group actions and rigidity theory for Anosov actions---as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.