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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Non-generic cusps


Authors: Michał Misiurewicz and Ana Rodrigues
Journal: Trans. Amer. Math. Soc. 363 (2011), 3553-3572
MSC (2010): Primary 37G15, 37E99
Published electronically: February 18, 2011
MathSciNet review: 2775818
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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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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
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

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05114-7
PII: S 0002-9947(2011)05114-7
Keywords: Cusp bifurcation, tongues, order of contact
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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.