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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Randomization of Sharkovskii-type theorems


Author: Jan Andres
Journal: Proc. Amer. Math. Soc. 136 (2008), 1385-1395
MSC (2000): Primary 37E05, 37E15, 37H10; Secondary 47H04, 47H40
Published electronically: December 18, 2007
Erratum: Proc. Amer. Math. Soc. 136 (2008), 3733-3734
MathSciNet review: 2367111
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Abstract: We formulate an abstract scheme for the randomization of Sharkovskii-type theorems via transformation to the deterministic case. In particular, Sharkovskii-type theorems for scalar differential equations can be randomized in this way. A random version of the standard Sharkovskii theorem is presented explicitly. Many remarks, comments and illustrating examples are supplied.


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Additional Information

Jan Andres
Affiliation: Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
Email: andres@inf.upol.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09242-8
PII: S 0002-9939(07)09242-8
Keywords: Sharkovskii-type theorems, randomization, transformation to deterministic case, random periodic orbits, transversal maps
Received by editor(s): February 14, 2007
Published electronically: December 18, 2007
Additional Notes: This work was supported by the Council of Czech Government (MSM 6198959214).
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.