Bolsinov, A. V. (Alekseĭ Viktorovich)
Overview
Works:  16 works in 68 publications in 3 languages and 748 library holdings 

Roles:  Author, Opponent 
Publication Timeline
.
Most widely held works by
A. V Bolsinov
Integrable Hamiltonian systems : geometry, topology, classification by
A. V Bolsinov(
Book
)
22 editions published between 2002 and 2004 in English and Undetermined and held by 325 WorldCat member libraries worldwide
"Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularities, and topological invariants."Jacket
22 editions published between 2002 and 2004 in English and Undetermined and held by 325 WorldCat member libraries worldwide
"Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularities, and topological invariants."Jacket
Geometry and dynamics of integrable systems by
A. V Bolsinov(
)
17 editions published in 2016 in English and German and held by 251 WorldCat member libraries worldwide
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemática in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to biHamiltonian systems; and the generalization of integrable systems to the nonHamiltonian settings. All three sections were written by top experts in their respective fields
17 editions published in 2016 in English and German and held by 251 WorldCat member libraries worldwide
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemática in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to biHamiltonian systems; and the generalization of integrable systems to the nonHamiltonian settings. All three sections were written by top experts in their respective fields
Integrable geodesic flows on twodimensional surfaces by
A. V Bolsinov(
Book
)
8 editions published between 1999 and 2000 in English and Russian and held by 85 WorldCat member libraries worldwide
8 editions published between 1999 and 2000 in English and Russian and held by 85 WorldCat member libraries worldwide
Topological methods in the theory of integrable systems(
Book
)
4 editions published in 2006 in English and held by 61 WorldCat member libraries worldwide
The third international conference of AMADE was held in Minsk, Belarus in September 2003 and covered key topics including integral transforms and special functions; differential equations and their applications; integral, difference, functional equations and fractional calculus; real and complex analysis. This volume comprises selected papers presented at this conference and provides a useful reference for graduates and researchers working in these areas of mathematics. The volume includes original papers devoted to the classification of singularities with symmetries, semiclassical integrability, construction of "exotic" integrable systems, applications of integrability to Riemannian geometry, and analysis of specific integrable systems in classical mechanics. All of the contributing authors are wellknown specialists actively working in this area of mathematics
4 editions published in 2006 in English and held by 61 WorldCat member libraries worldwide
The third international conference of AMADE was held in Minsk, Belarus in September 2003 and covered key topics including integral transforms and special functions; differential equations and their applications; integral, difference, functional equations and fractional calculus; real and complex analysis. This volume comprises selected papers presented at this conference and provides a useful reference for graduates and researchers working in these areas of mathematics. The volume includes original papers devoted to the classification of singularities with symmetries, semiclassical integrability, construction of "exotic" integrable systems, applications of integrability to Riemannian geometry, and analysis of specific integrable systems in classical mechanics. All of the contributing authors are wellknown specialists actively working in this area of mathematics
Vvedenie v topologii︠u︡ integriruemykh gamilʹtonovykh sistem by
A. V Bolsinov(
Book
)
3 editions published in 1997 in Russian and held by 9 WorldCat member libraries worldwide
3 editions published in 1997 in Russian and held by 9 WorldCat member libraries worldwide
Vvedenie v topologiju integriruemych gamilʹtonovych sistem by
A. V Bolsinov(
Book
)
2 editions published in 1997 in Russian and held by 3 WorldCat member libraries worldwide
2 editions published in 1997 in Russian and held by 3 WorldCat member libraries worldwide
Integrable geodesic flows on the suspension of toric automorphisms by
A. V Bolsinov(
Book
)
2 editions published in 1999 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 3 WorldCat member libraries worldwide
Integriruemye gamilʹtonovy sistemy : geometrii︠a︡, topologii︠a︡, klassifikat︠s︡ii︠a︡ by
A. V Bolsinov(
Book
)
1 edition published in 1999 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 1999 in Russian and held by 2 WorldCat member libraries worldwide
Topologicheskie metody v teorii gamilʹtonovykh sistem : sbornik stateĭ(
Book
)
1 edition published in 1998 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in Russian and held by 2 WorldCat member libraries worldwide
Riemannian metrics with integrable geodesic flows on surfaces : local and global geometry(
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
Topologičeskie metody v teorii gamilʹtonovych sistem : sbornik statej(
Book
)
1 edition published in 1998 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1998 in Russian and held by 1 WorldCat member library worldwide
Normalisation Cinfini des systèmes complètement intégrables by
Kai Jiang(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
This thesis is devoted to the local geometric linearization of completely integrable systems in the C1 category. The subject is the geometric linearization conjecture proposed (and proved in the analytic case) by Nguyen Tien Zung. We start from linear systems and introduce normalization in the formal category. Wes how that an integrable system can be decomposed into a hyperbolic part and an elliptic part. We establish a good PoincaréDulac normal form for the vector fields and discuss its relation with geometric linearization. We prove that weakly hyperbolic integrable systems are geometrically linearizable byusing Chaperon's tools. We then study integrable systems on small dimensional spaces: if the dimension is no more than 4, then most cases are geometrically linearizable; in particular,geometric linearization works for integrable system of focusfocus type. Finally, we generalize the proof to high dimensions and propose a condition about strongly invariant manifolds, under which we linearize the systems in the geometric sense. We also manage to normalize an R x Taction of several focuses by referring to the ideas of Zung
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
This thesis is devoted to the local geometric linearization of completely integrable systems in the C1 category. The subject is the geometric linearization conjecture proposed (and proved in the analytic case) by Nguyen Tien Zung. We start from linear systems and introduce normalization in the formal category. Wes how that an integrable system can be decomposed into a hyperbolic part and an elliptic part. We establish a good PoincaréDulac normal form for the vector fields and discuss its relation with geometric linearization. We prove that weakly hyperbolic integrable systems are geometrically linearizable byusing Chaperon's tools. We then study integrable systems on small dimensional spaces: if the dimension is no more than 4, then most cases are geometrically linearizable; in particular,geometric linearization works for integrable system of focusfocus type. Finally, we generalize the proof to high dimensions and propose a condition about strongly invariant manifolds, under which we linearize the systems in the geometric sense. We also manage to normalize an R x Taction of several focuses by referring to the ideas of Zung
Riemannian metrics with integrable geodesic flows on surfaces : local and global geometry by
A. V Bolsinov(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
Integrable Hamiltonian systems geometry, topology, classification by
A. V Bolsinov(
)
2 editions published in 2004 in English and held by 1 WorldCat member library worldwide
2 editions published in 2004 in English and held by 1 WorldCat member library worldwide
Integrable geodesic flows on the suspensions of toric automorphisms by
A. V Bolsinov(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Integriruemye gamilʹtonovye sistemy : geometrija ; topologija ; klassifikacija by
A. T Fomenko(
Book
)
1 edition published in 1997 in Undetermined and held by 0 WorldCat member libraries worldwide
1 edition published in 1997 in Undetermined and held by 0 WorldCat member libraries worldwide
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Related Identities
 Fomenko, A. T. Author
 Zung, Nguyen Tien 1970 Opponent
 Miranda, Eva Opponent Editor
 Morales Ruiz, Juan J. (Juan José) 1953
 Matveev, Vladimir Editor
 Oshemkov, A. A. (Andreĭ Aleksandrovich)
 Fomenko, Anatoly Timofeevič
 Springer International Publishing AG Publisher
 Taimanov, I. A.
 Matveev, Vladimir Borisovich 1944 Editor
Associated Subjects