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On principal iteration semigroups in the case of multiplier zero. (English) Zbl 1266.39021

Authors’ 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.

MSC:

39B12 Iteration theory, iterative and composite equations
26A18 Iteration of real functions in one variable
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