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Divisible, reciprocal automorphisms of the unit interval

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Abstract
The Cauchy equation for automorphisms of the unit interval is fulfilled only by the identity mapping. We consider two weakened forms of this Cauchy equation: the reciprocity equation and the n-divisibility equation. Although the solution sets of both functional equations are quite large, requiring that an automorphism is both reciprocal and n-divisible, drastically increases the set of obligatory fixed points. However, increasing n also enlarges the domain on which the automorphism can be chosen freely. We also describe the solution sets of two functional equations that arise by composing the reciprocity and n-divisibility property.
Keywords
divisibility, Reciprocity, Cauchy equation, Cantor set, automorphism

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Chicago
Maes, Koen, and Bernard De Baets. 2009. “Divisible, Reciprocal Automorphisms of the Unit Interval.” International Journal of Uncertainty Fuzziness and Knowledge-based Systems 17 (2): 221–235.
APA
Maes, Koen, & De Baets, B. (2009). Divisible, reciprocal automorphisms of the unit interval. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 17(2), 221–235.
Vancouver
1.
Maes K, De Baets B. Divisible, reciprocal automorphisms of the unit interval. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. 2009;17(2):221–35.
MLA
Maes, Koen, and Bernard De Baets. “Divisible, Reciprocal Automorphisms of the Unit Interval.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 17.2 (2009): 221–235. Print.
@article{692953,
  abstract     = {The Cauchy equation for automorphisms of the unit interval is fulfilled only by the identity mapping. We consider two weakened forms of this Cauchy equation: the reciprocity equation and the n-divisibility equation. Although the solution sets of both functional equations are quite large, requiring that an automorphism is both reciprocal and n-divisible, drastically increases the set of obligatory fixed points. However, increasing n also enlarges the domain on which the automorphism can be chosen freely. We also describe the solution sets of two functional equations that arise by composing the reciprocity and n-divisibility property.},
  author       = {Maes, Koen and De Baets, Bernard},
  issn         = {0218-4885},
  journal      = {INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS},
  language     = {eng},
  number       = {2},
  pages        = {221--235},
  title        = {Divisible, reciprocal automorphisms of the unit interval},
  url          = {http://dx.doi.org/10.1142/S0218488509005826},
  volume       = {17},
  year         = {2009},
}

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