Description

Book Synopsis

1 Remarks on the enumeration of plane curves.- 2 Remarks on the extatic points of plane curves.- 3 On the number of flattening points on space curves.- 4 Remarks on the parabolic curves on surfaces and on the higher-dimensional MöbiusSturm theory.- 5 Towards the Legendre Sturm theory of space curves.- 6 Topological problems of the theory of asymptotic curves.- 7 Simple singularities of curves.- 8 Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges.- 9 Topological classification of real trigonometric polynomials and cyclic serpents polyhedron.- 10 Topological problems of the theory of wave propagation.- 11 Topological content of the Maxwell theorem on multipole representation of spherical functions.- 12 Topologically necessary singularities on moving wavefronts and caustics.- 13 An appendix in the book Fewnomials by A.G. Khovanskii.- 14 Singularities of fractions and behavior of polynomials at infinity.- 15 Remarks concerning the Morse theory of a divergence-free vector field, the averaging method, and the motion of a charged particle in a magnetic field.- 16 On the problem of realization of a given Gaussian curvature function.- 17 Relatives of the quotient of the complex projective plane by the complex
conjugation.- 18 First steps of local symplectic algebra.- 19 First steps of local contact algebra.- 20 Higher-dimensional continued fractions.- 21 Weak asymptotics for the numbers of solutions of Diophantine problems.- 22 Mysterious mathematical trinities.- 23 The principle of topological economy in algebraic geometry.- 24 Translation of the V.I. Arnold paper From superpositions to KAM theory.- 25 From Hilbert's superposition problem to dynamical systems.- 25a Recollections (by Jurgen Moser).- 26 Symplectization, complexification and mathematical trinities.- 27 Topological problems in wave propagation theory and topological economy principle in algebraic geometry.- 28 Catastrophe theory.- 29 Mathematics and physics: mother and daughter or sisters?.- 30 Hard (rigid) and soft (flexible) mathematical models.- 31 Repartitioning the world: Population and the powers of two.- 32 On some problems of pseudo-periodic topology.- 33 Preface to the book Pseudoperiodic Topology.- 34 An interview with Vladimir Arnold (by S.H. Lui).- 35 Vershik work needs acknowledgement.- 35a On Arnold's Letter to the Notices of the AMS (by V.M. Vershik).- 36 The Russian edition of the works by David Hilbert.- 37 A disciple of the Moscow mathematical school has been awarded the Fields medal.- 38 About Vladimir Abramovich Rokhlin.- 39 Mathematics and mathematical education in the contemporary world.- 40 Mathematical illiteracy is more destructive than the fires of the inquisition.- 41 On teaching mathematics.- 42 Excerpts from the review of the textbook Mathematical Analysis.- 43 The antiscientific revolution and mathematics.- 44 Answers to the questionnaire of the European Mathematical Society.- 45 International mathematical congress in Berlin.- 46 Preface to the book International Congress of Mathematicians in Kyoto.- 47 Preface to the book International Congress of Mathematicians in Zürich.- 48 Preface to the Russian translation of the book Concrete Mathematics.- 49 On the epigraph to Eugene Onegin.- 49a On Arnold's and Pushkin's puzzles (by Boris Khesin).- Acknowledgements .

Vladimir I. Arnold Collected Works

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    A Hardback by Vladimir I. Arnold

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      Publisher: Springer
      Publication Date: Publication Date: 2/12/2025
      ISBN13: 9783031774843, 978-3031774843
      ISBN10: 3031774841

      Description

      Book Synopsis

      1 Remarks on the enumeration of plane curves.- 2 Remarks on the extatic points of plane curves.- 3 On the number of flattening points on space curves.- 4 Remarks on the parabolic curves on surfaces and on the higher-dimensional MöbiusSturm theory.- 5 Towards the Legendre Sturm theory of space curves.- 6 Topological problems of the theory of asymptotic curves.- 7 Simple singularities of curves.- 8 Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges.- 9 Topological classification of real trigonometric polynomials and cyclic serpents polyhedron.- 10 Topological problems of the theory of wave propagation.- 11 Topological content of the Maxwell theorem on multipole representation of spherical functions.- 12 Topologically necessary singularities on moving wavefronts and caustics.- 13 An appendix in the book Fewnomials by A.G. Khovanskii.- 14 Singularities of fractions and behavior of polynomials at infinity.- 15 Remarks concerning the Morse theory of a divergence-free vector field, the averaging method, and the motion of a charged particle in a magnetic field.- 16 On the problem of realization of a given Gaussian curvature function.- 17 Relatives of the quotient of the complex projective plane by the complex
      conjugation.- 18 First steps of local symplectic algebra.- 19 First steps of local contact algebra.- 20 Higher-dimensional continued fractions.- 21 Weak asymptotics for the numbers of solutions of Diophantine problems.- 22 Mysterious mathematical trinities.- 23 The principle of topological economy in algebraic geometry.- 24 Translation of the V.I. Arnold paper From superpositions to KAM theory.- 25 From Hilbert's superposition problem to dynamical systems.- 25a Recollections (by Jurgen Moser).- 26 Symplectization, complexification and mathematical trinities.- 27 Topological problems in wave propagation theory and topological economy principle in algebraic geometry.- 28 Catastrophe theory.- 29 Mathematics and physics: mother and daughter or sisters?.- 30 Hard (rigid) and soft (flexible) mathematical models.- 31 Repartitioning the world: Population and the powers of two.- 32 On some problems of pseudo-periodic topology.- 33 Preface to the book Pseudoperiodic Topology.- 34 An interview with Vladimir Arnold (by S.H. Lui).- 35 Vershik work needs acknowledgement.- 35a On Arnold's Letter to the Notices of the AMS (by V.M. Vershik).- 36 The Russian edition of the works by David Hilbert.- 37 A disciple of the Moscow mathematical school has been awarded the Fields medal.- 38 About Vladimir Abramovich Rokhlin.- 39 Mathematics and mathematical education in the contemporary world.- 40 Mathematical illiteracy is more destructive than the fires of the inquisition.- 41 On teaching mathematics.- 42 Excerpts from the review of the textbook Mathematical Analysis.- 43 The antiscientific revolution and mathematics.- 44 Answers to the questionnaire of the European Mathematical Society.- 45 International mathematical congress in Berlin.- 46 Preface to the book International Congress of Mathematicians in Kyoto.- 47 Preface to the book International Congress of Mathematicians in Zürich.- 48 Preface to the Russian translation of the book Concrete Mathematics.- 49 On the epigraph to Eugene Onegin.- 49a On Arnold's and Pushkin's puzzles (by Boris Khesin).- Acknowledgements .

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