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1.

図書
図書
1. Mathematical methods of classical mechanics (: us ; : gw)
V.I. Arnold ; translated by K. Vogtmann and A. Weinstein
出版情報: New York ; Berlin : Springer-Verlag, c1978  x, 462 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 60
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2.

図書
図書
2. The Arnoldfest : proceedings of a conference in honour of V.I. Arnold for his sixtieth birthday
Edward Bierstone ... [et al.], editors
出版情報: Providence, R.I. : American Mathematical Society, c1999  xvii, 555 p. ; 27 cm.
シリーズ名: Fields Institute communications ; 24
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目次情報: 続きを見る
From Hilbert's superposition problem to dynamical systems / V. I. Arnold
Recollections / J. Moser
Symplectization, complexification and mathematical trinities
Topological problems in wave propagation theory and topological economy principle in algebraic geometry
Geometry and control of three-wave interactions / M. S. Alber ; G. G. Luther ; J. E. Marsden ; J. M. Robbins
Standard basis along a Samuel stratum, and implicit differentiation / E. Bierstone ; P. D. Milman
A global weighted version of Bezout's theorem / J. Damon
Real Enriques surfaces without real points and Enriques-Einstein-Hitchin 4-manifolds / A. Degtyarev ; V. Kharlamov
On the index of a vector field at an isolated singularity / W. Ebeling ; S. M. Gusein-Zade
The exponential map on $\mathcal{D}^s_\mu$ / D. G. Ebin ; G. Misiolek
Zeldovich's neutron star and the prediction of magnetic froth / M. H. Freedman
Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds / K. Fukaya ; K. Ono
Multiplicity of a zero of an analytic function on a trajectory of a vector field / A. Gabrielov
Singularity theory and symplectic topology / A. B. Givental
On enumeration of meromorphic functions on the line / V. V. Goryunov ; S. K. Lando
Pseudoholomorphic curves and dynamics / H. Hofer ; E. Zehnder
Bifurcation of planar and spatial polycycles: Arnold's program and its development / Yu. S. Ilyashenko ; V. Yu. Kaloshin
Singularity which has no $M$-smoothing / V. M. Kharlamov ; S. Yu. Orevkov ; E. I. Shustin
Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces / B. Khesin ; A. Rosly
Newton polyhedra, a new formula for mixed volume, product of roots of a system of equations / A. Khovanskii
Interactions of Andronov-Hopf and Bogdanov-Takens bifurcations / W. F. Langford ; K. Zhan
Solutions of the qKZB equation in tensor products of finite dimensional modules over the elliptic quantum group $E_{\tau,\eta}sl_2$ / E. Mukhin ; A. Varchenko
Schrodinger operators on graphs and symplectic geometry / S. P. Novikov
On the dominant Fourier modes in the series associated with separatrix splitting for an a-priori stable, three degree-of-freedom Hamiltonian system / M. Rudnev ; S. Wiggins
Homology of $i$-connected graphs and invariants of knots, plane arrangements, etc. / V. A. Vassiliev
On Arnold's variational principles in fluid mechanics / V. A. Vladimirov ; K. I. Ilin
On functions and curves defined by ordinary differential equations / S. Yakovenko
Global finiteness properties of analytic families and algebra of their Taylor coefficients / Y. Yomdin
From Hilbert's superposition problem to dynamical systems / V. I. Arnold
Recollections / J. Moser
Symplectization, complexification and mathematical trinities
3.

図書
図書
3. Pseudoperiodic topology
Vladimir Arnold, Maxim Kontsevich, Anton Zorich, editors
出版情報: Providence, R.I. : American Mathematical Society, c1999  xii, 178 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 197 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 46
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On the topology of quasiperiodic functions / S. M. Gusein-Zade
Statistics of Klein polyhedra and multidimensional continued fractions / M. L. Kontsevich ; Yu. M. Suhov
$C^0$-generic properties of boundary operators in the Novikov complex / A. Pajitnov
Pseudoperiodic mappings / D. A. Panov
How do the leaves of a closed 1-form wind around a surface? / A. Zorich
On the topology of quasiperiodic functions / S. M. Gusein-Zade
Statistics of Klein polyhedra and multidimensional continued fractions / M. L. Kontsevich ; Yu. M. Suhov
$C^0$-generic properties of boundary operators in the Novikov complex / A. Pajitnov
4.

図書
図書
4. Bifurcation theory and catastrophe theory (: pbk)
V.I. Arnold ... [et al.]
出版情報: Berlin ; Tokyo : Springer-Verlag, c1999  271 p. ; 24 cm
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目次情報: 続きを見る
Preface
Bifurcations of Equilibria / Chapter 1：
Families and Deformations /   1：
Families of Vector Fields / 1.1：
The Space of Jets / 1.2：
Sard's Lemma and Transversality Theorems / 1.3：
Simplest Applications: Singular Points of Generic Vector Fields / 1.4：
Topologically Versal Deformations / 1.5：
The Reduction Theorem / 1.6：
Generic and Principal Families / 1.7：
Bifurcations of Singular Points in Generic One-Parameter Families /   2：
Typical Germs and Principal Families / 2.1：
Soft and Hard Loss of Stability / 2.2：
Bifurcations of Singular Points in Generic Multi-Parameter Families with Simply Degenerate Linear Parts /   3：
Principal Families / 3.1：
Bifurcation Diagrams of the Principal Families (3±) in Table 1 / 3.2：
Bifurcation Diagrams with Respect to Weak Equivalence and Phase Portraits of the Principal Families (4±) in Table 1 / 3.3：
Bifurcations of Singular Points of Vector Fields with a Doubly-Degenerate Linear Part /   4：
A List of Degeneracies / 4.1：
Two Zero Eigenvalues / 4.2：
Reductions to Two-Dimensional Systems / 4.3：
One Zero and a Pair ofPurely Imaginary Eigenvalues / 4.4：
Two Purely Imaginary Pairs / 4.5：
Principal Deformations of Equations of Difficult Type in Problems with Two Pairs of Purely Imaginary Eigenvalues (Following Żol&acedil;dek) / 4.6：
The Exponents of Soft and Hard Loss of Stability /   5：
Definitions / 5.1：
Table of Exponents / 5.2：
Bifurcations of Limit Cycles / Chapter 2：
Bifurcations of Limit Cycles in Generic One-Parameter Families
Multiplier 1
Multiplier - 1 and Period-Doubling Bifurcations
A Pair of Complex Conjugate Multipliers
Nonlocal Bifurcations in One-Parameter Families of Diffeomorphisms
Nonlocal Bifurcations of Periodic Solutions
Bifurcations Resulting in Destructions of Invariant Tori
Bifurcations of Cycles in Generic Two-Parameter Families with an Additional Simple Degeneracy
A Multiplier +1 or -1 with Additional Degeneracy in the Nonlinear Terms
A Pair of Multipliers on the Unit Circle with Additional Degeneracy in the Nonlinear Terms / 2.3：
Bifurcations of Cycles in Generic Two-Parameter Families with Strong Resonances of Orders q &neq; 4
The Normal Form in the Case of Unipotent Jordan Blocks
Averaging in the Seifert and the Möbius Foliations
Principal Vector Fields and their Deformations
Versality of Principal Deformations / 3.4：
Bifurcations of Stationary Solutions of Periodic Differential Equations with Strong Resonances of Orders q &neq; 4 / 3.5：
Bifurcations of Limit Cycles for a Pair of Multipliers Crossing the Unit Circle at ±i
Degenerate Families
Degenerate Families Found Analytically
Degenerate Families Found Numerically
Bifurcations in Nondegenerate Families
Limit Cycles of Systems with a Fourth Order Symmetry
Finitely-Smooth Normal Forms of Local Families
A Synopsis of Results
Definitions and Examples
General Theorems and Deformations of Nonresonant Germs / 5.3：
Reduction to Linear Normal Form / 5.4：
Deformations of Germs of Diffeomorphisms of Poincaré Type / 5.5：
Deformations of Simply Resonant Hyperbolic Germs / 5.6：
Deformations of Germs of Vector Fields with One Zero Eigenvalue at a Singular Point / 5.7：
Functional Invariants of Diffeomorphisms of the Line / 5.8：
Functional Invariants of Local Families of Diffeornorphisms / 5.9：
Functional Invariants of Families of Vector Fields / 5.10：
Functional Invariants of Topological Classifications of Local Families of Diffeomorphisms of the Line / 5.11：
Feigenbaum Universality for Diffeomorphisms and Flows /   6：
Period-Doubling Cascades / 6.1：
Perestroikas of Fixed Points / 6.2：
Cascades of n-fold Increases of Period / 6.3：
Doubling in Hamiltonian Systems / 6.4：
The Period-Doubling Operator for One-Dimensional Mappings / 6.5：
The Universal Period-Doubling Mechanism for Diffeomorphisms / 6.6：
Nonlocal Bifurcations / Chapter 3：
Degeneracies of Codimension 1. Summary of Results
Local and Nonlocal Bifurcations
Nonhyperbolic Singular Points
Nonhyperbolic Cycles
Nontransversal Intersections of Manifolds
Contours
Bifurcation Surfaces
Characteristics of Bifurcations
Summary of Results / 1.8：
Nonlocal Bifurcations of Flows on Two-Dimensional Surfaces /  2：
Semilocal Bifurcations of Flows on Surfaces
Nonlocal Bifurcations on a Sphere: The One-Parameter Case
Generic Families of Vector Fields
Conditions for Genericity / 2.4：
One-Parameter Families on Surfaces different from the Sphere / 2.5：
Global Bifurcations of Systems with a Global Transversal Section on a Torus / 2.6：
Some Global Bifurcations on a Klein bottle / 2.7：
Bifurcations on a Two-Dimensional Sphere: The Multi-Parameter Case / 2.8：
Some Open Questions / 2.9：
Bifurcations of Trajectories Homoclinic to a Nonhyperbolic Singular Point /  3：
A Node in its Hyperbolic Variables
A Saddle in its Hyperbolic Variables: One Homoclinic Trajectory
The Topological Bernoulli Automorphism
A Saddle in its Hyperbolic Variables: Several Homoclinic Trajectories
Bifurcations of Trajectories Homoclinic to a Nonhyperbolic Cycle
The Structure of a Family of Homoclinic Trajectories
Critical and Noncritical Cycles
Creation of a Smooth Two-Dimensional Attractor
Creation of Complex Invariant Sets (The Noncritical Case)
The Critical Case
A Two-Step Transition from Stability to Turbulence
A Noncompact Set of Homoclinic Trajectories / 4.7：
Intermittency / 4.8：
Accessibility and Nonaccessibility / 4.9：
Stability of Families of Diffeomorphisms / 4.10：
Hyperbolic Singular Points with Homoclinic Trajectories / 4.11：
Preliminary Notions: Leading Directions and Saddle Numbers
Bifurcations of Homoclinic Trajectories of a Saddle that Take Place on the Boundary of the Set of Morse-Smale Systems
Requirements for Genericity
Principal Families in <$>{\op R}^3<$> and their Properties
Versality of the Principal Families
A Saddle with Complex Leading Direction in <$>{\op R}^3<$>
An Addition: Bifurcations of Homoclinic Loops Outside the Boundary of a Set of Morse-Smale Systems
An Addition: Creation of a Strange Attractor upon Bifurcation of a Trajectory Homoclinic to a Saddle
Bifurcations Related to Nontransversal Intersections
Vector Fields with No Contours and No Homoclinic Trajectories
A Theorem on Inaccessibility
Moduli
Systems with Contours
Diffeomorphisms with Nontrivial Basic Sets
Vector Fields in <$>{\op R}^3<$> with Trajectories Homoclinic to a Cycle
Symbolic Dynamics / 6.7：
Bifurcations of Smale Horseshoes / 6.8：
Vector Fields on a Bifurcation Surface / 6.9：
Diffeomorphisms with an Infinite Set of Stable Periodic Trajectories / 6.10：
Infinite Nonwandering Sets /   7：
Vector Fields on the Two-Dimensional Torus / 7.1：
Bifurcations of Systems with Two Homoclinic Curves of a Saddle / 7.2：
Systems with Feigenbaum Attractors / 7.3：
Birth of Nonwandering Sets / 7.4：
Persistence and Smoothness of Invariant Manifolds / 7.5：
The Degenerate Family and Its Neighborhood in Function Space / 7.6：
Birth of Tori in a Three-Dimensional Phase Space / 7.7：
Attractors and their Bifurcations /   8：
The Likely Limit Set According to Milnor (1985) / 8.1：
Statistical Limit Sets / 8.2：
Internal Bifurcations and Crises of Attractors / 8.3：
Internal Bifurcations and Crises of Equilibria and Cycles / 8.4：
Bifurcations of the Two-Dimensional Torus / 8.5：
Relaxation Oscillations / Chapter 4：
Fundamental Concepts
An Example: van der Pol's Equation
Fast and Slow Motions
The Slow Surface and Slow Equations
The Slow Motion as an Approximation to the Perturbed Motion
The Phenomenon of Jumping
Singularities of the Fast and Slow Motions
Singularities of Fast Motions at Jump Points of Systems with One Fast Variable
Singularities of Projections of the Slow Surface
The Slow Motion for Systems with One Slow Variable
The Slow Motion for Systems with Two Slow Variables
Normal Forms of Phase Curves of the Slow Motion
Connection with the Theory of Implicit Differential Equations
Degeneration of the Contact Structure
The Asymptotics of Relaxation Oscillations
Degenerate Systems
Systems of First Approximation
Normalizations of Fast-Slow Systems with Two Slow Variables for ε > 0
Derivation of the Systems of First Approximation
Investigation of the Systems of First Approximation
Funnels / 3.6：
Periodic Relaxation Oscillations in the Plane / 3.7：
Delayed Loss of Stability as a Pair of Eigenvalues Cross the Imaginary Axis
Generic Systems
Delayed Loss of Stability
Hard Loss of Stability in Analytic Systems of Type 2
Hysteresis
The Mechanism of Delay
Computation of the Moment of Jumping in Analytic Systems
Delay Upon Loss of Stability by a Cycle
Delayed Loss of Stability and "Ducks"
Duck Solutions
An Example: A Singular Point on the Fold of the Slow Surface
Existence of Duck Solutions
The Evolution of Simple Degenerate Ducks
A Semi-local Phenomenon: Ducks with Relaxation
Ducks in <$>{\op R}^3<$> and <$>{\op R}^n<$>
Recommended Literature
References
Additional References
Preface
Bifurcations of Equilibria / Chapter 1：
Families and Deformations /   1：
5.

図書
図書
5. Singularities : the Brieskorn anniversary volume (: sz ; : us)
V.I. Arnold, G.-M. Greuel, J.H.M. Steenbrink, editors
出版情報: Basel ; Boston : Birkhäuser Verlag, c1998  xxv, 458 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 162
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6.

図書
図書
6. Topological methods in hydrodynamics (: hbk)
Vladimir I. Arnold, Boris A. Khesin
出版情報: New York : Springer, c1998  xv, 374 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 125
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7.

図書
図書
7. Geometrical methods in the theory of ordinary differential equations. 2nd ed (: us ; : gw)
V.I. Arnold ; translated by Joseph Szücs ; English translation edited by Mark Levi
出版情報: New York ; Tokyo : Springer-Verlag, c1988  xii, 351 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 250
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Special Equations
First-Order Partial Differential Equations
Structural Stability
Perturbation Theory
Normal Forms
Local Bifurcation Theory
Samples of Examination Problems
Index
Special Equations
First-Order Partial Differential Equations
Structural Stability
8.

図書
図書
8. Topics in singularity theory : V.I. Arnold's 60th anniversary collection
A. Khovanskiĭ, A. Varchenko, V. Vassiliev, editors ; [translation edited by A.B. Sossinsky]
出版情報: Providence, R.I. : American Mathematical Society, c1997  xiii, 255 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 180 . Advances in the mathematical sciences (formerly Advances in Soviet Mathematics) ; 34
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9.

図書
図書
9. The Arnold-Gelfand mathematical seminars : [geometry and singularity theory] (: us ; : sz)
V.I. Arnold ... [et al.], editors
出版情報: Boston : Birkhäuser, c1997  vi, 437 p. ; 25 cm
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10.

図書
図書
10. Singularities and bifurcations
V.I. Arnold, editor
出版情報: Providence, R.I. : American Mathematical Society, c1994  x, 262 p. ; 27 cm
シリーズ名: Advances in Soviet mathematics ; v. 21
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