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Irregular solutions of the Feigenbaum functional equation

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Języki publikacji
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Abstrakty
EN
We describe the structure of orbits generated by two commuting bijections and using this description we construct irregular solutions of the Feigenbaum functional equation. The graph of such a solution almost cover the plane in the sense of measure and topology.
Wydawca
Rocznik
Strony
135--141
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] K. Baron and P. Volkmann, Dense sets of additive functions, Seminar LV, No. 16 (2003), 4 pp., http://www.mathematik.uni-ka rlsruhe.de/˜semlv
  • [2] L. Bartłomiejczyk, Solutions with big big graph of iterative functional equations, Real Analysis Exch., 24th Summer Symposium Conference Reports, May 2000, 133-135.
  • [3] L. Bartłomiejczyk, Solutions with big graph of an equation of the second iteration, Aequationes Math. 62 (2001), 309-317.
  • [4] L. Bartłomiejczyk, Irregular solutions of the Feigenbaum functional equation, 26th Summer Symposium Conference Reports, June 2002, 103-106.
  • [5] J. P. R. Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255-260.
  • [6] J. P. R. Christensen, Topology and Borel Structure, North-Holland Mathematical Studies 10, North-Holland Publishing Company & American Elsevier Publishing Company, Amsterdam-London-New York, 1974.
  • [7] P. R. Halmos, Measure Theory, Graduate Texts in Mathematics 18, Springer-Verlag, New York-Heidelberg-Berlin, 1974.
  • [8] F. B. Jones, Connected and disconnected plane sets and the functional equation f(x) + f(y) = f(x + y), Bull. Amer. Math. Soc. 48 (1942), 115-120.
  • [9] P. Kahlig and J. Smital, On the solutions of a functional equation of Dhombres, Results Math. 27 (1995), 362-367 .
  • [10] A. S. Kechris, Classical Descriptive Set Theory, Graduate Texts in Mathematics 156, Springer-Verlag, New York-Berlin-Heidelberg, 1994.
  • [11] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, Prace Naukowe Uniwersytetu Śląskiego w Katowicach 489, Państwowe Wydawnictwo Naukowe & Uniwersytet Śląski, Warszawa-Kraków-Katowice, 1985.
  • [12] K. Kuratowski and A. Mostowski, Set Theory, Studies in Logic and Foundations of Mathematics 86, PWN-Polish Scientific Publishers and North-Holland Publishing Company, Warszawa-Amsterdam-New York-Oxford, 1976.
  • [13] J. C. Oxtoby, Measure and Category, Graduate Text in Mathematics 2, Springer Verlag, New York-Heidelberg-Berlin, 1971.
  • [14] K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York-San Francisco-London, 1967.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0012-0014
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