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Uspekhi Mat. Nauk, 1996, Volume 51, Issue 1(307), Pages 3–50 (Mi umn919)  

This article is cited in 20 scientific papers (total in 21 papers)

Topological problems of the theory of wave propagation

V. I. Arnol'dab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Université Paris-Dauphine

DOI: https://doi.org/10.4213/rm919

Full text: PDF file (532 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1996, 51:1, 1–47

Bibliographic databases:

UDC: 514
MSC: 58J47, 65T40, 42A10, 57R17
Received: 04.09.1995

Citation: V. I. Arnol'd, “Topological problems of the theory of wave propagation”, Uspekhi Mat. Nauk, 51:1(307) (1996), 3–50; Russian Math. Surveys, 51:1 (1996), 1–47

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Arnol'd, “Topological Classification of Trigonometric Polynomials and Combinatorics of Graphs with an Equal Number of Vertices and Edges”, Funct. Anal. Appl., 30:1 (1996), 1–14  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. I. Arnol'd, “Remarks on the Parabolic Curves on Surfaces and on the Higher-Dimensional Möbius–Sturm Theory”, Funct. Anal. Appl., 31:4 (1997), 227–239  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    4. B. Z. Shapiro, “On the number of connected components of the space of trigonometric polynomials of degree $n$ with $2n$ different critical values”, Math. Notes, 62:4 (1997), 529–534  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Senechal M., “Two communities and vertical integration”, Mathematical Intelligencer, 19:2 (1997), 33–37  crossref  mathscinet  zmath  isi
    6. Shapiro, B, “Discriminants of convex curves are homeomorphic”, Proceedings of the American Mathematical Society, 126:7 (1998), 1923  crossref  mathscinet  zmath  isi
    7. Arnol'd, VI, “Mathematics and physics: mother and daughter or sisters?”, Uspekhi Fizicheskikh Nauk, 169:12 (1999), 1311  mathnet  crossref  isi
    8. Tabachnikov, S, “Fagnano orbits of polygonal dual billiards”, Geometriae Dedicata, 77:3 (1999), 279  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Jürgen Ehlers, Ezra T. Newman, “The theory of caustics and wave front singularities with physical applications”, J Math Phys (N Y ), 41:6 (2000), 3344  crossref  mathscinet  isi  scopus  scopus
    10. D. A. Panov, “Special Points of Surfaces in the Three-Dimensional Projective Space”, Funct. Anal. Appl., 34:4 (2000), 276–287  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Tabachnikov, S, “A four vertex theorem for polygons”, American Mathematical Monthly, 107:9 (2000), 830  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Au, TKK, “Off-center reflections: Caustics and chaos”, Experimental Mathematics, 10:2 (2001), 287  crossref  mathscinet  isi  scopus  scopus
    13. Uribe-Vargas, R, “Weak convexity does not imply convexity for curves in RPn, n > 2”, Comptes Rendus Mathematique, 335:1 (2002), 47  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Borovskikh, AV, “The eiconal equation in an inhomogeneous medium”, Doklady Mathematics, 68:1 (2003), 103  zmath  isi  elib
    15. A. V. Borovskikh, “Group classification of the eikonal equation for a 3-dimensional inhomogeneous medium”, Sb. Math., 195:4 (2004), 479–520  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Uribe-Vargas, R, “Four-vertex theorems, Sturm theory and Lagrangian singularities”, Mathematical Physics Analysis and Geometry, 7:3 (2004), 223  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. P. E. Pushkar', Yu. V. Chekanov, “Combinatorics of fronts of Legendrian links and the Arnol'd 4-conjectures”, Russian Math. Surveys, 60:1 (2005), 95–149  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. Galaktionov V.A., Harwin P.J., “Sturm's theorems on zero sets in nonlinear parabolic equations”, Sturm-Liouville Theory: Past and Present, 2005, 173–199  crossref  mathscinet  zmath  isi
    19. R. Uribe-Vargas, “A projective invariant for swallowtails and godrons, and global theorems on the flecnodal curve”, Mosc. Math. J., 6:4 (2006), 731–768  mathnet  crossref  mathscinet  zmath
    20. Proc. Steklov Inst. Math., 258 (2007), 178–193  mathnet  crossref  mathscinet  zmath  elib
    21. Balk P.I., Dolgal A.S., “Generalized Solutions of the Inverse Problem and New Technologies For the Quantitative Interpretation of Gravity Anomalies”, Izv.-Phys. Solid Earth, 54:2 (2018), 372–387  crossref  isi  scopus  scopus
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