Trofimov, V. V. 1952
Overview
Works:  19 works in 58 publications in 2 languages and 566 library holdings 

Roles:  Author, Editor, htt 
Classifications:  QA312, 517.3 
Publication Timeline
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Most widely held works by
V. V Trofimov
Introduction to geometry of manifolds with symmetry by
V. V Trofimov(
Book
)
15 editions published between 1994 and 2011 in English and held by 227 WorldCat member libraries worldwide
One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the threedimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of nonEuclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral fourdimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour dimensional spacetime, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated
15 editions published between 1994 and 2011 in English and held by 227 WorldCat member libraries worldwide
One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the threedimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of nonEuclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral fourdimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour dimensional spacetime, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated
Integrable systems on Lie algebras and symmetric spaces by
A. T Fomenko(
Book
)
11 editions published between 1987 and 1998 in English and held by 172 WorldCat member libraries worldwide
11 editions published between 1987 and 1998 in English and held by 172 WorldCat member libraries worldwide
Tensor and vector analysis : geometry, mechanics, and physics by
A. T Fomenko(
Book
)
8 editions published between 1996 and 1998 in English and held by 127 WorldCat member libraries worldwide
8 editions published between 1996 and 1998 in English and held by 127 WorldCat member libraries worldwide
Vvedenie v geometrii︠u︡ mnogoobraziĭ s simmetrii︠a︡mi by
V. V Trofimov(
Book
)
1 edition published in 1989 in Russian and held by 12 WorldCat member libraries worldwide
1 edition published in 1989 in Russian and held by 12 WorldCat member libraries worldwide
Vvedenie v geometriju mnogoo'razij s simmetrijami by
V. V Trofimov(
Book
)
4 editions published in 1989 in Russian and held by 4 WorldCat member libraries worldwide
4 editions published in 1989 in Russian and held by 4 WorldCat member libraries worldwide
Dynamical systems by
A. T Fomenko(
)
1 edition published in 1993 in English and held by 4 WorldCat member libraries worldwide
This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment ofthe geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. Other surveys treat various aspects of integrable Hamiltonian systems, with an emphasis on Liealgebraic constructions. Among the topics covered are: the generalized CalogeroMoser systems based on root systems of simple Lie algebras, a ge neral rmatrix scheme for constructing integrable systems and Lax pairs, links with finitegap integration theory, topologicalaspects of integrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems (Toda lattices) using the machinery of representation theory. Readers will find all the new differential geometric and Liealgebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics
1 edition published in 1993 in English and held by 4 WorldCat member libraries worldwide
This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment ofthe geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. Other surveys treat various aspects of integrable Hamiltonian systems, with an emphasis on Liealgebraic constructions. Among the topics covered are: the generalized CalogeroMoser systems based on root systems of simple Lie algebras, a ge neral rmatrix scheme for constructing integrable systems and Lax pairs, links with finitegap integration theory, topologicalaspects of integrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems (Toda lattices) using the machinery of representation theory. Readers will find all the new differential geometric and Liealgebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics
Geometric measure theory by
Herbert Federer(
Book
)
3 editions published in 1987 in Russian and held by 3 WorldCat member libraries worldwide
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society
3 editions published in 1987 in Russian and held by 3 WorldCat member libraries worldwide
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society
Integrable systems on Lie algebras and symmetric speces by
A. T Fomenko(
Book
)
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
Vvedenie v geometriû mnogoobrazij s simmetriâmi [Texte imprimé] by
V. V Trofimov(
Book
)
1 edition published in 1989 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in Russian and held by 2 WorldCat member libraries worldwide
Vvedenie v geometriû mnogoobrazij s simmetriâmi by
V. V Trofimov(
Book
)
2 editions published in 1989 in Russian and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in Russian and held by 2 WorldCat member libraries worldwide
Algebra i geometrija integriruemych gamilʹtonovych differencialʹnych uravnenij by
V. V Trofimov(
Book
)
2 editions published between 1992 and 1995 in Russian and held by 2 WorldCat member libraries worldwide
2 editions published between 1992 and 1995 in Russian and held by 2 WorldCat member libraries worldwide
Algebra i geometria integriruemyh gamilʹtonovyh differencialʹnyh uravnenij by
V. V Trofimov(
Book
)
1 edition published in 1995 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1995 in Russian and held by 1 WorldCat member library worldwide
Algebra i geometrii︠a︡ integriruemykh gamilʹtonovykh different︠s︡ialʹnykh uravneniĭ by
V. V Trofimov(
Book
)
1 edition published in 1995 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1995 in Russian and held by 1 WorldCat member library worldwide
Simmetricheskie prostranstva by
Ottmar Loos(
Book
)
1 edition published in 1985 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1985 in Russian and held by 1 WorldCat member library worldwide
O redkih životnyh mira : kniga dlâ učaŝihsâ by
Igor' Petrovič Sosnovskij(
Book
)
1 edition published in 1987 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1987 in Russian and held by 1 WorldCat member library worldwide
Algebra i geometrija integriruemyh gamiljtonovyh differencialjnyh uravnenij by
V. V Trofimov(
Book
)
1 edition published in 1995 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1995 in Russian and held by 1 WorldCat member library worldwide
Sovremennyj russkij literaturnyj âzyk : Morfologiâ by
V. V Trofimov(
Book
)
2 editions published in 1957 in Russian and held by 1 WorldCat member library worldwide
2 editions published in 1957 in Russian and held by 1 WorldCat member library worldwide
Sovremennyj russkij literaturnyj âzyk : Fonetika, grafika by
V. V Trofimov(
Book
)
2 editions published in 1957 in Russian and held by 1 WorldCat member library worldwide
2 editions published in 1957 in Russian and held by 1 WorldCat member library worldwide
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Audience Level
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Related Identities
 Fomenko, A. T. Author Editor
 Manturov, O. V. Editor
 Weisman, A. Translator
 Rayfield, P. D. Translator
 Karaulov, A. Translator
 Perelomov, A. M.
 Gershkovich, V. Ya
 Okuneva, G.G.
 Reyman, A.G.
 Arnol'd, V. I.
Associated Subjects
Calculus of tensors Chaotic behavior in systems Differentiable dynamical systems Differential equations Geometric measure theory Geometry Geometry, Differential Global differential geometry Hamiltonian systems Hyperbolic spaces Lie algebras Manifolds (Mathematics) Mathematics Measure theory Nonholonomic dynamical systems Symmetric spaces Symmetry Symplectic manifolds Topological groups Vector analysis
Covers
Alternative Names
Trofimov, V. V.
Trofimov, V. V. 1952
Trofimov, Valerii V. 1952
Trofimov, Valeriĭ Vladimirovich 1952
Trofimov, Valerij Vladimirovich 1952
Trofimov, Valery Vladimirovich
Trofimov, Valery Vladimirovitch
Трофимов, Валерий Владимирович
Трофимов, Валерий Владимирович 1952...
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