Polynomials hardly commuting with increasing bijections

Kannan, V. ; Sankararao, B. ; Subramania Pillai, I. ; Niketa Salvi, S. (2008) Polynomials hardly commuting with increasing bijections Semigroup Forum, 76 (1). pp. 124-132. ISSN 0037-1912

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Official URL: http://www.springerlink.com/content/67524477u4l086...

Related URL: http://dx.doi.org/10.1007/s00233-007-9031-7


Let I be an interval in the real line R. Among the real polynomials that take I to I, we ask which ones do not commute with any increasing bijection of I other than identity. For this purely algebraic problem, the solution involves concepts in topological dynamics. Our main characterizations are in terms of full orbits of critical points and periodic points. Using these, we obtain simpler criterion, namely, that for no nontrivial subinterval K ⊂ I, the successive images {f n (K):n=0,1,2,...} form a pairwise disjoint collection. This problem is of interest in topological dynamics because it is about characterization of polynomials with unique self-topological-conjugacy.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Preperiodic Point; Precritical Point; Topological-conjugacy
ID Code:15572
Deposited On:13 Nov 2010 12:54
Last Modified:03 Jun 2011 07:35

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