Category Archives: Topology

Download Modern Geometry - Methods and Applications: Part 3: by B.A. Dubrovin PDF

By B.A. Dubrovin

During the last fifteen years, the geometrical and topological tools of the idea of manifolds have assumed a significant function within the so much complicated parts of natural and utilized arithmetic in addition to theoretical physics. the 3 volumes of "Modern Geometry - equipment and purposes" include a concrete exposition of those equipment including their major functions in arithmetic and physics. This 3rd quantity, offered in hugely available languages, concentrates in homology idea. It comprises introductions to the modern tools for the calculation of homology teams and the class of manifesto. either scientists and scholars of arithmetic in addition to theoretical physics will locate this booklet to be a helpful reference and textual content.

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Download Introduction to the Qualitative Theory of Dynamical Systems by G. R. Belitsky, and E. V. Zhuzhoma S. Kh. Aranson PDF

By G. R. Belitsky, and E. V. Zhuzhoma S. Kh. Aranson

This publication is an creation to the qualitative idea of dynamical structures on manifolds of low size (on the circle and on surfaces). besides classical effects, it displays the main major achievements during this quarter received in recent years by way of Russian and international mathematicians whose paintings has no longer but seemed within the monographic literature. the most rigidity here's wear worldwide difficulties within the qualitative idea of flows on surfaces.

Despite the truth that flows on surfaces have an analogous neighborhood constitution as flows at the aircraft, they've got many international homes intrinsic to multidimensional platforms. this is often attached regularly with the lifestyles of nontrivial recurrent trajectories for such flows. The research of dynamical structures on surfaces is as a result a common degree within the transition to multidimensional dynamical systems.

The reader of this e-book desire be ordinary simply with simple classes in differential equations and gentle manifolds. all of the major definitions and ideas required for realizing the contents are given within the text.

The effects expounded can be utilized for investigating mathematical types of mechanical, actual, and different structures (billiards in polygons, the dynamics of a spinning best with nonholonomic constraints, the constitution of liquid crystals, etc.).

In our opinion the ebook can be priceless not just to mathematicians in all parts, but in addition to experts with a mathematical history who're learning dynamical methods: mechanical engineers, physicists, biologists, and so on.

Readership: Graduate scholars and researchers operating in dynamical structures and differential equations, in addition to experts with a mathematical heritage who're learning dynamical procedures: mechanical engineers, physicists, biologists, and so forth.

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Download Dynamical Systems, Ergodic Theory and Applications by L.A. Bunimovich, S.G. Dani, R.L. Dobrushin, M.V. Jakobson, PDF

By L.A. Bunimovich, S.G. Dani, R.L. Dobrushin, M.V. Jakobson, I.P. Kornfeld, N.B. Maslova, Ya.B. Pesin, Ya.G. Sinai, J. Smillie, Yu.M. Sukhov, A.M. Vershik

This EMS quantity, the 1st variation of which used to be released as Dynamical structures II, EMS 2, units out to familiarize the reader to the elemental rules and result of glossy ergodic idea and its purposes to dynamical structures and statistical mechanics. The exposition starts off from the elemental of the topic, introducing ergodicity, blending and entropy. The ergodic concept of delicate dynamical structures is handled. a number of examples are awarded conscientiously in addition to the guidelines underlying an important effects. in addition, the e-book offers with the dynamical platforms of statistical mechanics, and with numerous kinetic equations. For this moment enlarged and revised variation, released as Mathematical Physics I, EMS a hundred, new contributions on ergodic idea of flows on homogeneous manifolds and on tools of algebraic geometry within the thought of period trade differences have been further. This booklet is obligatory studying for all mathematicians operating during this box, or desirous to find out about it.

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Download Riemannian geometry in an orthogonal frame by Vladislav V Goldberg, Shiing-Shen Chern PDF

By Vladislav V Goldberg, Shiing-Shen Chern

Foreword via S S Chern
In 1926-27, Cartan gave a sequence of lectures within which he brought external types on the very starting and used largely orthogonal frames all through to enquire the geometry of Riemannian manifolds. during this direction he solved a chain of difficulties in Euclidean and non-Euclidean areas, in addition to a chain of variational difficulties on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of those Cartan's lectures and released them as a publication entitled Riemannian Geometry in an Orthogonal body. This publication has many inventions, resembling the inspiration of intrinsic general differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional area or in an area of continuous curvature, an affine connection outlined in a typical fiber package deal of a submanifold, and so forth. It has now been translated into English via Vladislav V Goldberg, at present exotic Professor of arithmetic on the New Jersey Institute of know-how, united states, who additionally edited the Russian version.

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Download Three-Dimensional Geometry and Topology by William P. Thurston PDF

By William P. Thurston

This publication develops a few of the remarkable richness, good looks, and gear of geometry in and 3 dimensions, and the powerful connection of geometry with topology. Hyperbolic geometry is the big name. a robust attempt has been made to show not only denatured formal reasoning (definitions, theorems, and proofs), yet a residing feeling for the topic. there are numerous figures, examples, and workouts of various trouble.

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Download Poisson Geometry, Deformation Quantisation and Group by Simone Gutt, John Rawnsley, Daniel Sternheimer PDF

By Simone Gutt, John Rawnsley, Daniel Sternheimer

Poisson geometry lies on the cusp of noncommutative algebra and differential geometry, with typical and demanding hyperlinks to classical physics and quantum mechanics. This e-book offers an creation to the topic from a small workforce of best researchers, and the result's a quantity available to graduate scholars or specialists from different fields. The contributions are: Poisson Geometry and Morita Equivalence via Bursztyn and Weinstein; Formality and big name items by means of Cattaneo; Lie Groupoids, Sheaves and Cohomology through Moerdijk and Mrcun; Geometric equipment in illustration thought through Schmid; Deformation thought: a robust software in Physics Modelling via Sternheimer.

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Download Fixed Point Theory and Applications by Ravi P. Agarwal, Maria Meehan, Donal O’Regan PDF

By Ravi P. Agarwal, Maria Meehan, Donal O’Regan

This transparent exposition of the flourishing box of fastened element thought, a big software within the fields of differential equations and useful equations, begins from the fundamentals of Banach's contraction theorem and develops lots of the major effects and methods. The publication explores many functions of the idea to research, with topological concerns enjoying a very important position. The very huge bibliography and shut to a hundred workouts suggest that it may be used either as a textual content and as a accomplished reference paintings, presently the one one in every of its style.

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