On Half Iterates of Functions Defined on Finite Sets

• Autorzy: Kozyra P. M.

Identyfikatory

DOI

10.12921/cmst.2018.0000027

• Języki publikacji: EN

Abstrakty

EN

Four algorithms determining all functional square roots (half iterates) and seven algorithms finding one functional square root of any function f : X → X defined on a finite set X, if these square roots exist, are presented herein. Time efficiency of these algorithms depending on the complexity of examined functions is compared and justification of correctness is given. Moreover, theorems which make finding half iterates possible in some cases or facilitate this task are formulated.

Słowa kluczowe

EN

functional square root; half iterate; iterated function

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2018
• Tom: Vol. 24, No. 3
• Strony: 187--209
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Kozyra P. M.

• Institute of Mathematics University of Silesia in Katowice Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] J. Gross, J. Yellen, Handbook of Graph Theory, CRC Press,2003.
• [2] M.N.S. Swamy, K. Thulasiraman, Graphs: Theory and Algorithms. Wiley, 1992.
• [3] Kneser, H. Reelle analytische Lösungen der GleichungΦ(Φ(x)) = ex und verwandter Funktionalgleichungen. Journalfur die reine und angewandte Mathematik. 187, 56–67 (1950).
• [4] Gray J., Parshall, K. Episodes in the History of Modern Algebra (1800–1950), American Mathematical Society, ISBN 978-0-8218-4343-7, 2007.
• [5] E. Schröder, Über iterirte Functionen. Mathematische Annalen, 3 (2), 296–322 (1870).
• [6] G. Szekeres, Regular iteration of real and complex functions Acta Mathematica 100, (3–4) 361–376 (1958).
• [7] T. Curtright, C. Zachos, X. Jin, Approximate solutions of functional equations, Journal of Physics A 44 (40): 405205 (2011).
• [8] M.C. Zdun, On iterative roots of homeomorphisms of the circle, Bull. Pol. Acad. Sci. Math 48 (2), 203-213.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).