{"title":"Marcelo Viana","description":"","products":[{"product_id":"differential-equations-book-marcelo-viana-9781470465407","title":"Differential Equations","description":"This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time--pure and applied alike--ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman-Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincare-Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49741167264017,"sku":"NGR9781470465407","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/147046540X.jpg?v=1763483019"},{"product_id":"lectures-on-lyapunov-exponents-book-marcelo-viana-9781107081734","title":"Lectures on Lyapunov Exponents","description":"The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51019563073809,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51019565334801,"sku":"NIN9781107081734","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52410214908177,"sku":"NLS9781107081734","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/B01M5CVW49.jpg?v=1750709883"},{"product_id":"marcelo-viana-selected-works-book-marcelo-viana-9783031019715","title":"Marcelo Viana - Selected Works","description":"Dynamical systems and the twin field ergodic theory have their roots in the qualitative theory of differential equations, developed by the great mathematician Henri Poincaré, and in the kinetic theory of gases built in mathematical terms by physicists James Clerk Maxwell and Ludwig Boltzmann. Together, they aim to model, explain and predict the behavior of natural and artificial phenomena which evolve in time.  For more than three decades, Marcelo Viana has been making several outstanding contributions to this area of mathematics. This volume contains a selection of his research papers, covering a wide range of topics: rigorous theory of strange attractors, physical measures, bifurcation theory, homoclinic phenomena, fractal dimensions, partial hyperbolicity, thermodynamic formalism, non-uniform hyperbolicity, interval exchange maps Teichmüller flows, and the modern theory of Lyapunov exponents.    Marcelo Viana, a world leader in this field, has been the object of several academic distinctions, such as the inaugural Ramanujan prize of the International Centre for Theoretical Physics, and the Louis D. Scientific Grand Prix of the Institut de France. He is also recognized for his broad contribution to the mathematical community, in his country and region as well as in the international arena.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":53689931006225,"sku":"NIN9783031019715","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031019715.jpg?v=1781976337"}],"url":"https:\/\/www.worldofbooks.com\/en-au\/collections\/author-books-by-marcelo-viana.oembed","provider":"World of Books ","version":"1.0","type":"link"}