Vladimir I. Arnold - Collected Works

Publisher Springer

Format

eBook

2nd Edition 1st Edition

Quantity

Add New

Publisher

Springer

Volume

Copyright

2014

ISBN13

9783642310317

Release

Format

eBook

Grade Level

College Freshman - College Senior

DDC
TBD

Overview

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
Front Cover.
Half Title Page.
Other Frontmatter.
Other Frontmatter.
Other Fromtmatter.
Title Page.
Copyright Page.
Preface.
Acknowledgements.
Contents.
Other Frontmatter.
1: Variational Principle for Three-Dimensional Steady-State Flows of an Ideal Fluid.
2: On the Riemann Curvature of Diffeomorphism Groups.
3: Topologie. — Sur La Topologie Des écoulements Stationnaires Des Fluides Parfaits. Note (*) De M. Vladimir Arnold, Présentée Par m. Jean Leray..
4: Conditions for Non-Linear Stability of Stationary Plane Curvilinear Flows of an Ideal Fluid.
5: On the Topology of Three-Dimensional Steady Flows of an Ideal Fluid.
6: On an Apriori Estimate in the Theory of Hydrodynamical Stability.
7: On the Differential Geometry of Infinite-Dimensional Lie Groups and Its Applications to the Hydrodynamics of Perfect Fluids∗.
8: On a Variational Principle for the Steady Flows of Perfect Fluids and Its Applications to Problems of Non-Linear Stability.
9: Characteristic Class Entering in Quantization Conditions.
10: A Note on Weierstrass' Auxiliary Theorem.
11: The Stability Problem and Ergodic Properties for Classical Dynamical System.
12: A Remark on the Ramification of Hyperelliptic Integrals as Functions of Parameters.
13: Singularities of Smooth Mappings.
14: Remarks on Singularities of Finite Codimension in Complex Dynamical Systems.
15: Braids of Algebraic Functions and the Cohomology of Swallowtails.
16: Hamiltonian Nature of the Euler Equations in the Dynamics of a Rigid Body and of an Ideal Fluid.
17: On the One-Dimensional Cohomology of the Lie Algebra of Divergence-Free Vector Fields and Rotation Numbers of Dynamical Systems.
18: The Cohomology Ring of the Colored Braids Group.
19: On Cohomology Classes of Algebraic Functions Invariant under Tschirnhausen Transformations.
20: Trivial Problems.
21: Algebraic Unsolvability of the Problem of Stability and the Problem of Topological Classification of Singular Points of Analytic Syste
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Vladimir I. Arnold - Collected Works

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