On principal iteration semigroups in the case of multiplier zero

Dorota Krassowska; Marek Zdun

Open Mathematics (2013)

  • Volume: 11, Issue: 1, page 177-187
  • ISSN: 2391-5455

Abstract

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We collect and generalize various known definitions of principal iteration semigroups in the case of multiplier zero and establish connections among them. The common characteristic property of each definition is conjugating of an iteration semigroup to different normal forms. The conjugating functions are expressed by suitable formulas and satisfy either Böttcher’s or Schröder’s functional equation.

How to cite

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Dorota Krassowska, and Marek Zdun. "On principal iteration semigroups in the case of multiplier zero." Open Mathematics 11.1 (2013): 177-187. <http://eudml.org/doc/269039>.

@article{DorotaKrassowska2013,
abstract = {We collect and generalize various known definitions of principal iteration semigroups in the case of multiplier zero and establish connections among them. The common characteristic property of each definition is conjugating of an iteration semigroup to different normal forms. The conjugating functions are expressed by suitable formulas and satisfy either Böttcher’s or Schröder’s functional equation.},
author = {Dorota Krassowska, Marek Zdun},
journal = {Open Mathematics},
keywords = {Schröder’s functional equation; Böttcher’s equation; Iteration semigroup; Conjugacy; Böttcher’s functional equation; iteration semigroup; conjugacy; normal forms; conjugating functions},
language = {eng},
number = {1},
pages = {177-187},
title = {On principal iteration semigroups in the case of multiplier zero},
url = {http://eudml.org/doc/269039},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Dorota Krassowska
AU - Marek Zdun
TI - On principal iteration semigroups in the case of multiplier zero
JO - Open Mathematics
PY - 2013
VL - 11
IS - 1
SP - 177
EP - 187
AB - We collect and generalize various known definitions of principal iteration semigroups in the case of multiplier zero and establish connections among them. The common characteristic property of each definition is conjugating of an iteration semigroup to different normal forms. The conjugating functions are expressed by suitable formulas and satisfy either Böttcher’s or Schröder’s functional equation.
LA - eng
KW - Schröder’s functional equation; Böttcher’s equation; Iteration semigroup; Conjugacy; Böttcher’s functional equation; iteration semigroup; conjugacy; normal forms; conjugating functions
UR - http://eudml.org/doc/269039
ER -

References

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  1. [1] Blanton G., Baker J.A., Iteration groups generated by C n functions, Arch. Math. (Brno), 1982, 18(3), 121–127 Zbl0518.26002
  2. [2] Ger J., Smajdor A., Regular iteration in the case of multiplier zero, Aequationes Math., 1972, 7, 127–131 http://dx.doi.org/10.1007/BF01818507 Zbl0243.39006
  3. [3] Kuczma M., Functional Equations in a Single Variable, Monogr. Mat., 46, PWN, Warszawa, 1968 
  4. [4] Kuczma M., Choczewski B., Ger R., Iterative Functional Equations, Encyclopedia Math. Appl., 32, Cambridge University Press, Cambridge, 1990 http://dx.doi.org/10.1017/CBO9781139086639 Zbl0703.39005
  5. [5] Szekeres G., Regular iteration of real and complex functions, Acta Math., 1958, 100, 203–258 http://dx.doi.org/10.1007/BF02559539 Zbl0145.07903
  6. [6] Targonski Gy., Topics in Iteration Theory, Studia Math.: Skript, 6, Vandenhoeck & Ruprecht, Göttingen, 1981 
  7. [7] Weitkämper J., Embeddings in iteration group and semigroups with nontrivial units, Stochastica, 1983, 7(3), 175–195 Zbl0567.39001
  8. [8] Zdun M.C., On the regular solutions of a linear functional equation, Ann. Polon. Math., 1974, 30, 89–96 
  9. [9] Zdun M.C., Some remarks on iteration semigroups, Uniw. Slaski w Katowicach Prace Naukowe-Prace Mat., 7, 1977, 65–69 
  10. [10] Zdun M.C., Continuous and Differentiable Iteration Semigroups, Prace Nauk. Uniw. Slask. Katowic., 308, Uniwersytet Slaski, Katowice, 1979 
  11. [11] Zdun M.C., On differentiable iteration groups, Publ. Math. Debrecen, 1979, 26(1–2), 105–114 Zbl0434.39004
  12. [12] Zdun M.C., On the structure of iteration group of homeomorphisms having fixed points, Aequationes Math., 1998, 55(3), 199–216 http://dx.doi.org/10.1007/s000100050030 Zbl0908.39007
  13. [13] Zdun M.C., Zhang W., Koenigs embedding flow problem with global C 1 smoothness, J. Math. Anal. Appl., 2011, 374(2), 633–643 http://dx.doi.org/10.1016/j.jmaa.2010.08.075 Zbl1213.37030

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