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Indices of some adjacencies of types and wavefront singularities.

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Τίτλος: Indices of some adjacencies of types and wavefront singularities.
Συγγραφείς: Sedykh, V. D.1 (AUTHOR) vdsedykh@gmail.com
Πηγή: Theoretical & Mathematical Physics. Sep2026, Vol. 228 Issue 3, p1653-1674. 22p.
Θεματικοί όροι: *Mathematical singularities, *Eikonal equation, *Mathematical functions, *Fiber bundles (Mathematics)
Περίληψη: We study simple stable wavefront singularities of a generic Legendrian map (e.g., for a wavefront propagation described by the eikonal equation in the cotangent bundle). The indices of adjacencies of singularities of types and to singularities whose preimages contain singular points of corank are calculated. The calculations are based on the classification of singularities of the Legendrian germ of type that we obtain in this paper. Finally, we discuss the application of our results to the problem of classifying curves that appear as a result of small deformations of singular real curves in the plane. [ABSTRACT FROM AUTHOR]
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  Data: Indices of some adjacencies of types and wavefront singularities.
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  Data: *<searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br />*<searchLink fieldCode="DE" term="%22Eikonal+equation%22">Eikonal equation</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br />*<searchLink fieldCode="DE" term="%22Fiber+bundles+%28Mathematics%29%22">Fiber bundles (Mathematics)</searchLink>
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  Data: We study simple stable wavefront singularities of a generic Legendrian map (e.g., for a wavefront propagation described by the eikonal equation in the cotangent bundle). The indices of adjacencies of singularities of types and to singularities whose preimages contain singular points of corank are calculated. The calculations are based on the classification of singularities of the Legendrian germ of type that we obtain in this paper. Finally, we discuss the application of our results to the problem of classifying curves that appear as a result of small deformations of singular real curves in the plane. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.1134/S0040577926090114
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 22
        StartPage: 1653
    Subjects:
      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Eikonal equation
        Type: general
      – SubjectFull: Mathematical functions
        Type: general
      – SubjectFull: Fiber bundles (Mathematics)
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            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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