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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Non-generic cusps
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by Michał Misiurewicz and Ana Rodrigues PDF
Trans. Amer. Math. Soc. 363 (2011), 3553-3572 Request permission

Abstract:

We find the order of contact of the boundaries of the cusp for two-parameter families of vector fields on the real line or diffeomorphisms of the real line, for cusp bifurcations of codimensions 1 and 2. Moreover, we create a machinery that can be used for the same problem in higher codimensions and perhaps for other, similar problems.
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Additional Information
  • Michał Misiurewicz
  • Affiliation: Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216 – and – Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
  • MR Author ID: 125475
  • Email: mmisiure@math.iupui.edu
  • Ana Rodrigues
  • Affiliation: Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216 – and – CMUP, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
  • Address at time of publication: Matematiska Institutionen, KTH, SE-100 44 Stockholm, Sweden
  • Email: arodrig@math.iupui.edu, amdsar@kth.se
  • Received by editor(s): December 14, 2008
  • Received by editor(s) in revised form: April 23, 2009
  • Published electronically: February 18, 2011
  • Additional Notes: The first author was partially supported by NSF grant DMS 0456526.
    The second author was supported by FCT Grant BPD/36072/2007. Research of the second author was supported in part by Centro de Matemática da Universidade do Porto (CMUP) financed by FCT through the programmes POCTI and POSI, with Portuguese and European Community structural funds.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3553-3572
  • MSC (2010): Primary 37G15, 37E99
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05114-7
  • MathSciNet review: 2775818