Vladimir I. Arnold - Collected Works, 1st Edition

  • Published By:
  • ISBN-10: 3642310311
  • ISBN-13: 9783642310317
  • DDC: 532.5
  • Grade Level Range: College Freshman - College Senior
  • 465 Pages | eBook
  • Original Copyright 2014 | Published/Released July 2014
  • This publication's content originally published in print form: 2014

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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.

Table of Contents

Front Cover.
Half Title Page.
Other Frontmatter.
Other Frontmatter.
Other Fromtmatter.
Title Page.
Copyright Page.
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 Systems of Differential Equations (Russian).
22: On Some Topological Invariants of Algebraic Functions1).
23: Topological Invariants of Algebraic Functions ii.
24: Algebraic Unsolvability of the Problem of Lyapunov Stability and the Problem of Topological Classification of Singular Points of an Analytic System of Differential Equations.
25: On the Arrangement of Ovals of Real Plane Algebraic Curves, Involutions of Four-Dimensional Smooth Manifolds, and the Arithmetic of Integral Quadratic Forms.
26: Topology of Real Algebraic Curves (Works of I.g. Petrovsky and Their Development)∗.
27: On Matrices Depending on Parameters.
28: Lectures on Bifurcations in Versal Families.
29: Versal Families and Bifurcations of Differential Equations (Russian).
30: Notes on the Three Dimensional Flow Pattern of a Perfect Fluid in the Presence of a Small Perturbation of the Initial Velocity Field.
31: The Asymptotic Hopf Invariant and Its Application*.
32: A Magnetic Field in a Moving Conducting Fluid.
33: A Magnetic Field in a Stationary Flow with Stretching in Riemannian Space.
34: Steady-State Magnetic Field in a Periodic Flow.
35: Some Remarks on the Antidynamo Theorem.
36: Evolution of a Magnetic Field under the Action of Transfer and Diffusion.
37: The Growth of a Magnetic Field in a Three-Dimensional Steady Incompressible Flow.
38: On Evolution of a Magnetic Field under the Action of Drift and Diffusion (Russian).
39: Exponential Scattering of Trajectories and Its Hydrodynamical Applications.
40: Kolmogorov's Hydrodynamic Attractors.
41: Topological Methods in Hydrodyamics.
42: Translator’s Preface to J. Milnor’s Book “morse Theory”.
43: Henri Poincaré: Selected Works in Three Volumes: Vol. I. New Methods of Celestial Mechanics.
44: Comments on the Paper “on a Geometric Theorem” by Henri Poincaré.