Displaying similar documents to “Embeddings in iteration groups and semigroups with nontrivial units.”

On principal iteration semigroups in the case of multiplier zero

Dorota Krassowska, Marek Zdun (2013)

Open Mathematics

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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.

Concave iteration semigroups of linear set-valued functions

Jolanta Olko (1999)

Annales Polonici Mathematici

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We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.

The structure of disjoint iteration groups on the circle

Krzysztof Ciepliński (2004)

Czechoslovak Mathematical Journal

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The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle 𝕊 1 , that is, families ℱ = { F v 𝕊 1 ⟶ 𝕊 1 v ∈ V } of homeomorphisms such that F v 1 ∘ F v 2 = F v 1 + v 2 , v 1 , v 2 ∈ V , and each F v either is the identity mapping or has no fixed point ( ( V , + ) is an arbitrary 2 -divisible nontrivial (i.e., c a r d V > 1 ) abelian group).