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Centre symmetry sets of families of plane curves

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Języki publikacji
EN
Abstrakty
EN
We study centre symmetry sets and equidistants for a 1-parameter family of plane curves where, for a special member of the family, there exist two inflexions with parallel tangents. Some results can be obtained by reducing a generating family to normal forms, but others require direct calculation from the generating family.
Wydawca
Rocznik
Strony
167--192
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
  • Department of Mathematical Sciences, The University of Liverpool, L69 7zl, Uk, pjgiblin@liv.ac.uk
autor
Bibliografia
  • [1] V. I. Arnol’d, Wavefront evolution and equivariant Morse lemma, Comm. Pure Appl. Math. 29 (1976), 557–582.
  • [2] V. I. Arnol’d, Singularities of Caustics and Wave Fronts, Math. Appl. Soviet Ser., 62, Kluwer, Dordrecht, 1990.
  • [3] V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Birkhäuser, 1988.
  • [4] J. W. Bruce, A classification of 1-parameter families of map germs R3, 0 → R3, 0, with applications to condensation problems, J. London Math. Soc. 33 (1986), 375–384.
  • [5] J. W. Bruce, P. J. Giblin, Curves and Singularities, Cambridge University Press, Second edition, 1992.
  • [6] W. Domitrz, P. de M. Rios, Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds, Geom. Dedicata 169 (2014), 361–382.
  • [7] P. J. Giblin, P. A. Holtom, The centre symmetry set, Geometry and Topology of Caustics, Banach Center Publications 50, ed. S. Janeczko and V. M. Zakalyukin, Warsaw, 1999, 91–105.
  • [8] P. J. Giblin, V. M. Zakalyukin, Singularities of centre symmetry sets, Proc. London Math. Soc. 90 (2005), 132–166.
  • [9] P. J. Giblin, V. M. Zakalyukin, Recognition of centre symmetry set singularities, Geom. Dedicata 130 (2007), 43–58.
  • [10] S. Janeczko, Bifurcations of the center of symmetry, Geom. Dedicata 60 (1996), 9–16.
  • [11] G. M. Reeve, Singularities of Systems of Chords in Affine space, PhD Thesis, University of Liverpool, 2012.
  • [12] G. M. Reeve, V. M. Zakalyukin, Singularities of the Minkowski set and affine equidistants for a curve and a surface, Topology Appl. 159 (2012), 555–561.
  • [13] G. M. Reeve, V. M. Zakalyukin, Affine chord envelopes for two surfaces in four space , Proc. Steklov Inst. Math. 277 (2012), 230–242.
  • [14] G. M. Reeve, V. M. Zakalyukin, Propagations from a space curve in three space with indicatrix a surface, J. Singularities 6 (2012), 131–145.
  • [15] G. Wassermann, Stability of unfoldings in space and time, Acta Math. 135 (1975), 57–128.
  • [16] V. M. Zakalyukin, Reconstructions of fronts and caustics depending on a parameter, and versality of mappings, J. Soviet Math. 27 (1984), 2713–2735.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fd8907bf-1de5-4a89-8c70-27a9a915aea3
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