Global analysis : studies and applications  v. 1 ~ v. 5

edited by Yu.G. Borisovich and Yu.E. Gliklikh

This volume, a sequel to volumes 1108, 1214 and 1334, is a selection of survey or expository articles on recent work in global analysis. These articles centre on methods of global analysis in nonlinear equations and topological and geometrical methods of analysis. An account by V.M.Tikhomirov on the life and work of A.N.Kolmogorov is included as a tribute to his influence on the development of mathematics.

「Nielsen BookData」より

lder spaces.

「Nielsen BookData」より

[目次]

  • Cauchy indices and the index of a singular point of a vector field.- Complete integrability with noncommuting integrals of certain euler equations.- Multidimensional parametrized variational problems on riemannian manifolds.- On certain classes of selections of many-valued mappings.- On the spectral synthesis in the spaces of solutions of invariant differential equations.- Topological aspects of geometrical theory of differential equations.- On the principle of the shortest way in the dynamics of systems with constraints.- Stochastic equations and differential geometry.- Fundamental physical equations uniquely determined by their symmetry groups.- Riemannian parallel translation, the ito integral, and stochastic equations on manifolds.- An equivariant analogue of the index of a gradient vector field.- On the topology of invertible linear singular integral operators.- Model equation for dynamics of phase translation.- The destruction of spherical symmetry in non-linear variational problems.

「Nielsen BookData」より

[目次]

  • Plateau operator and bifurcations of two-dimensional minimal surfaces.- Homological methods in the theory of periodic and equivariant maps.- Theory of operators and real algebraic geometry.- On the structure of the set of solutions for inclusions with multivalued operators.- Schouten bracket and canonical algebras.- Multidimensional sleeping tops.- Laplace-radon integral operators and singularities of solutions of differential equations on complex manifolds.- On the number of solutions for certain boundary-value problems.- Contact structure, relaxation oscillations and singular points of implicit differential equations.- Topological index estimates.- Modern approach to the theory of topological characteristics of nonlinear operators I.- Qualitative geometrical theory of integrable systems. classification of isoenergetic surfaces and bifurcation of liouville tori at the critical energy values.- Geometrical aspects of nelson's stochastic quantization.- Singularities of solutions of differential equations on complex manifolds (characteristical case).- Image of period mapping for simple singularities.- The geometry of the nonholonomic sphere for three-dimensional lie group.

「Nielsen BookData」より

[目次]

  • Semigroups dependent on a parameter, their attractors and asymptotic behaviour.- A modern approach to the theory of topological characteristics of non-linear operators. II.- Exact round morse functions, inequalities of morse type and integrals of Hamiltonian systems.- Estimates for ? - Balls of nonholonomic metrics.- The bifurcation of stationary rotations of a multidimensional asymmetric rigid body from the sleeping top regime.- Nonlocal integral manifolds and decoupling of nonlinear parabolic systems.- On Leary's residue theory.- Spencer cohomology of differential equations.- The properness of elliptic and parabolic differential operators.- A.N.Kolmogorov and the progress of mathematics.- On the completeness of left-invariant pseudo-Riemannian metrics on lie groups.- Second-order parabolic equations in principal fibre bundles and associated vector bundles.- Lyapunov-schmidt method and types of singularities of critical points of key function in the problem of bifurcations of minimal surfaces.- Relative topological characteristics of mappings.- On some problems from the theory of fixed points of multivalued mappings.- Relative calibrations and the problem of stability of minimal surfaces.- On topological questions of real complexity theory and combinatorial optimization.- Deformation and cohomologies of Poisson brackets.- Holomorphic rigidity of polynomial polyhedrons and quasihomogeneity.- On the structure of the set of solutions of a non-linear elliptic problem with fixed boundary conditions.

「Nielsen BookData」より

[目次]

  • Stochastic analysis, groups of diffemorphisms and lagrangian description of viscous incompressible fluid.- From topological homology: algebras with different properties of homological triviality.- Duality in stable spencer cohomologies.- On some problems of computational geometry and topology.- to Maslov's operational method (non-commutative analysis and differential equations).- The problem of realization of homology classes from Poincare up to the present.- Oriented degree of Fredholm maps of non-negative index and its application to global bifurcation of solutions.- Fuchsian systems with reducible monodromy and the Riemann-Hilbert problem.- Finitely smooth normal forms of vector fields in the vicinity of a rest point.- Generalized degree of multi-valued mappings.- On fredholmian aspects of linear transmission problems.- Stationary solutions of nonlinear stochastic equations.- Continuation of solutions to elliptic equations and localization of singularities.- Properness of nonlinear elliptic differential operators in Holder spaces.

「Nielsen BookData」より

[目次]

  • Topological theory of fixed points on infinite-dimensional manifolds.- The structure of extension orbits of lie algebras.- Branching of solutions of smooth Fredholm equations.- Characteristic Cauchy problem on a complex-analytic manifold.- Category of nonlinear differential equations.- Algebraic structure of certain integrable hamiltonian systems.- Riemannian parallel translation in non-linear mechanics.- On Hamiltonian systems with dynamical symmetries.- On the theory of generalized condensing perturbations of continuous mappings.- On solvability of non-linear equations with fredholm operators.- On certain properties of extremals in variational problems.- Minimal morse functions.- Topological methods of investigation of general nonlinear elliptical boundary value problems.- The contact geometry and linear differential equations.- Classical and non-classical dynamics with constraints.

「Nielsen BookData」より

この本の情報

書名 Global analysis : studies and applications
著作者等 Borisovich, I︠U︡. G.
Gliklikh, I︠U︡. E.
Borisovich Yuri G
Borisovich Yurii G.
Borisovich Yurii G
Catalano C E
Gliklikh Y E
Gliklikh Yuri E.
Gliklikh Yuri E
Gliklikh Yurii E
Vershik A M
Vershik A. M.
Borisovich Y G
書名別名 Analiz na mnogoobraziyakh i differentsialʹnye uravneniya

Primenenie topologii v sovremennom analize
シリーズ名 Lecture notes in mathematics
巻冊次 v. 1
v. 2
v. 3
v. 4
v. 5
出版元 Springer-Verlag
刊行年月 c1984-c1992
ページ数 v.
大きさ 25 cm
ISBN 0387139109
0387168214
0387500197
0387534075
0387555838
3540168214
3540500197
3540534075
3540555838
3540139109
NCID BA00289481
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言語 英語
原文言語 ロシア語
出版国 ドイツ
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